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Neutron-Proton cross section measurements in the intermediate energy range Keeler, Richard Kirk 1981

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Neutron-Proton Cross Section Measurements i n the Intermediate Energy Range by RICHARD KIRK KEELER B 7 SC., M c G i l l U n i v e r s i t y , 1976 M.Sc, University of B r i t i s h Columbia, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (PHYSICS) We accept t h i s t hesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1980 Q Richard Kirk Keeler, 1980 In presenting th is thes is in pa r t i a l fu l f i lment of the requirements f o r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f r ee l y ava i l ab le for reference and s t u d y . I fur ther agree that permission for extensive copying o f th is t h e s i s for scho la r l y purposes may be granted by the Head o f my Department or by h is representat ives . It is understood that c o p y i n g o r p u b l i c a t i o n o f th is thes is for f inanc ia l gain sha l l not be allowed without my writ ten permiss ion. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date i i Abstract Measurements of the angular d i s t r i b u t i o n and t o t a l reaction rate i n neutron-proton sc a t t e r i n g are described. The emphasis of t h i s work has been to obtain an accurate normalization of the d i s t r i b u t i o n , which i s d i f f i c u l t to achieve with neutral beams. Nearly monoenergetic neutrons from the d(p,n)pp reaction were scattered from a l i q u i d hydrogen target. The neutron beam energy was determined from the time of f l i g h t with respect to the radio frequency s i g n a l of the TRIUMF cyclotron. The d i f f e r e n t i a l cross section was measured at 319 and 493 MeV from 10 to 180 degrees i n the centre of mass (CM.). Calibrated neutron beam monitors upstream of the sc a t t e r i n g target provided an absolute normalization over the whole angular range. Between 10 and 100 degrees CM. a neutron detector consisting of a charged p a r t i c l e veto, a carbon convertor and two t r i g g e r s c i n t i l l a t o r s sandwiching 7 multiwire proportional chambers was used to select e l a s t i c neutrons by time of f l i g h t techniques. The neutron angular d i s t r i b u t i o n was measured with an average p r e c i s i o n of 5% and an uncertainty on the normalization of 1.3%. An associated p a r t i c l e experiment (neutrons and r e c o i l protons detected i n coincidence) determined the e f f i c i e n c y of the neutron detector and the monitors were c a l i b r a t e d by measuring the incident neutron f l u x with the neutron detector i n the beam, i . e . at zero degrees. The r e c o i l protons were detected i n the angular range between 60 and 180 degrees CM. with a p r e c i s i o n of 1% to 2% and an error on the normalization of 2.8% at 319 MeV and 3.7% at 493 MeV. E l a s t i c events were selected by time of f l i g h t and by e i t h e r a measurement of magnetic r i g i d i t y (momentum) or t o t a l energy. i i i The absolute normalization of the two experimental techniques i s v e r i f i e d by the overlap of the two measurements and by comparing the integrated d i f f e r e n t i a l cross section with the measured t o t a l cross section. The neutron-proton t o t a l cross section was measured at s i x energies between 200 and 500 MeV by a transmission type experiment to a p r e c i s i o n of 1% to 3%. The systematic corrections were small, of the order of 1%, and the s t a t i s t i c a l errors were increased to include monitor and beam i n s t a b i l i t i e s . The measurements show a smooth quadratic energy dependence. The data was included i n a phase s h i f t analysis and a dispersion r e l a t i o n analysis along with the previous world data. Agreement between the r e a l part of the forward s c a t t e r i n g amplitude predicted by the phase s h i f t analysis and by the dispersion r e l a t i o n analysis i s improved. The errors on the 1=0 (i s o s c a l a r ) phase s h i f t s are decreased and to a lesser extent on the 1=1 phase s h i f t s . There i s a marked improvement i n the smooth v a r i a t i o n with energy of the 1=0 phase s h i f t s and a better agree-ment of the higher p a r t i a l waves with the t h e o r e t i c a l predictions of the Paris p o t e n t i a l . i v Acknowledgements I would l i k e to thank my colleagues i n the BASQUE group: David Axen, Ed Auld, David Bugg, Tony Clough, Martin Comyn, John Edgington, Richard Dubois, Reg Gibson, George Ludgate, Reg Richardson, Lyle Robertson and Noel Stewart. I have enjoyed working with them for the past four years. I am very g r a t e f u l f o r the help of my friends who provided valuable discussion, constructive c r i t i c i s m and general support. Special thanks go to Joanne Steven who helped with the figures and checked the manu-s c r i p t . I also thank Martin Comyn for checking the manuscript. I would l i k e to thank David Bugg f or c a l c u l a t i n g some of the corrections and f o r c a r e f u l l y checking the numerical c a l c u l a t i o n s of thi s t h e s i s . My sincerest thanks go to David Axen, my supervisor, f o r the physics he has taught me and the guidance he gave me i n completing t h i s t h e s i s . V I dedicate t h i s thesis to my parents. v i TABLE OF CONTENTS Page I. Introduction 1 1-1. H i s t o r i c a l Background 1 1-2. Scattering Formalism 2 1-3. Complete Set of Experiments 8 1-4. Density Matrix Formalism 11 1-5. Experimental Observables ••• 16 1-6. Phase S h i f t Parametrization 16 1-7. Phenomenological Pot e n t i a l s 22 1-8. Experimental Review 23 1-9. BASQUE Programme to Determine the 1=0 Phase S h i f t s ... 24 1-10. The Cross Section Measurements 25 1-11. Previous Normalization Techniques 28 I- 12. Organization of Thesis 28 II . Neutron Scattering F a c i l i t y 31 I I - l . Cyclotron 31 II-2. Beam Line 31 II-3. Primary Proton Beam Monitor 33 II-4. Liquid Deuterium Target — 37 II-5. 4AB2 Dipole Magnet 37 II-6. Neutron Collimator 41 II-7. Neutron Beam Monitors 41 II-8. Sweep Magnet ... .................................. 45 II-9. Shadow Collimator .................................... 45 11-10. Liq u i d Hydrogen Target ............................... 47 11-11. Multiwire Proportional Chambers ...................... 50 11-12. Helium Bags .......................................... 50 v i i Page I I I . D i f f e r e n t i a l Cross Section Experiment 52 I I I - l . D i f f e r e n t i a l Cross Section Measured by Detecting Neutrons 52 I I I - 2. D i f f e r e n t i a l Cross Section Measured by Detecting Rec o i l Protons ••• 64 IV. Analysis of D i f f e r e n t i a l Cross Section Data 74 IV- 1. Analysis of Neutron Data 74 IV-2. Analysis of the Magnetic Spectrometer Data 93 IV- 3. T o t a l Energy Spectrometer 114 V. Corrections and Systematic Errors 120 V- l . Target Length 120 V-2. Target Density 120 V-3. Neutron Beam Attenuation 121 V-4. Corrections to the Neutron Signal 121 V-5. Corrections to the Zero Degree Data 130 V-6. Corrections of E f f i c i e n c y Measurements 130 V-7. Corrections to Proton Data - Magnetic Spectrometer ... 130 V-8. Corrections to Proton Data - T o t a l Energy Spectrometer 137 V-9. Error Analysis f or the Neutron Signal 140 V-10. Error Analysis of the Proton Signal - Magnetic Spectrometer 149 V - l l . Error Analysis of the Proton Signal — T o t a l Energy Spectrometer 151 V-12. Normalization Error 151 V-13. Results of the D i f f e r e n t i a l Cross Section Measurement. 162 V-14. Overlap of Forward and Backward Data and the T o t a l Cross Section Constraint 169 v i i i Page VI. T o t a l Cross Section Experiment 175 VI-1. Introduction to P r i n c i p l e s of Experimental Method . — 175 VI-2. Apparatus and R e a l i z a t i o n 178 VI-3. Of f-line Analysis i 8 4 VI- 4. Corrections and Systematic E f f e c t s 191 VII. Discussion of Data and Conclusions l ^ 8 VII- 1. D i f f e r e n t i a l Cross Section at Energies near 319 MeV .. 198 VII-2. D i f f e r e n t i a l Cross Section at Energies near 493 MeV .. 2 0 2 VII-3. T o t a l Cross Section Data between 200 and 530 MeV 2 0 5 VII-4. Phase S h i f t Analysis 2 1 0 VII-5. Conclusions 2 2 1 i x FIGURES Page 1-1. Co-ordinates and Kinematics of N-N Scattering 4 1-2. D i f f e r e n t i a l Cross Section and Wolfenstein P o l a r i z a t i o n Parameters 14 1-3. Wolfenstein Pol a r i z a t i o n - T r a n s f e r Parameters 15 1- 4. Phase S h i f t Chart 20 2- 1. Cyclotron and Beam Transport 32 2-2. Schematic of Primary Proton Beam Monitor 34 2-3. E l e c t r o n i c Logic for Primary Proton Beam Monitor 35 2-4. PI to RF TOF Spectrum f o r a Typ i c a l Run at 493 MeV 38 2-5. Liquid Deuterium Target 39 2-6. Schematic of the Neutron Collimator System 42 2-7. Schematic of Neutron Beam Monitors 44 2-8. E l e c t r o n i c Logic of Neutron Beam Monitors 46 2-9. Neutron Beam P r o f i l e 48 2- 10. Liquid Hydrogen Target 49 3- 1. Schematic of Apparatus used to Measure Scattered Neutrons .. 53 3-2. I l l u s t r a t i o n of PV Hodoscope 54 3-3. E l e c t r o n i c Logic f o r the Neutron Detector 57 3-4. E l e c t r o n i c Logic f o r the Computer Trigger 59 3-5. On-line. E f f i c i e n c y Histogram 61 3-6. On-line PI to P2 Histogram 62 3-7. On-line PI to RF Histogram 63 3-8. Schematic of Apparatus used to Measure Recoi l Protons -Magnetic Spectrometer 65 3-9. E l e c t r o n i c Logic f o r the Recoil Proton Experiment .......... 69 X Page 3- 10. Schematic of Apparatus used to Measure R e c o i l Protons - T o t a l Energy Spectrometer 7 2 4- 1. PI to P2 Time of F l i g h t Spectrum 7 5 4-2. PI to RF Time of F l i g h t Spectrum 7 7 4-3. Horizontal D i s t r i b u t i o n of Events over the Carbon Convert or 8 0 4-4. V e r t i c a l D i s t r i b u t i o n of Events over the Carbon Convertor .. 81 4-5. Histogram of the Scattering Angle i n the Carbon 8 3 4-6. S i m p l i f i e d Perspective of Neutron Detector I l l u s t r a t i n g V a r i a t i o n of E f f i c i e n c y as a function of P o s i t i o n on Carbon 8 4 4-7. Flow Chart of Cuts i n Neutron Analysis 8 ^ 4-8. E f f i c i e n c y Data and F i t Plotted as a Function of Inverse K i n e t i c Energy 92 4-9. Flow Chart of Cuts i n Magnetic Spectrometer Analysis 96 4-10. Histogram of Difference Between Incident and Exit Track Intercepts 98 4-11. Li q u i d Hydrogen Target P r o f i l e 99 4-12. Histogram of Bend Angle 1 0 1 4-13. Scatter Plot of the SI to S3 TOF vs. Momentum 1 Q 4 4-14. Scatter Plot of the S2 to RF TOF vs. Momentum 1 0 5 4-15. Maximum Energy of I n e l a s t i c Protons as a Function of Lab Angle f o r 319 and 493 MeV Incident Neutrons 1 0 7 4-16. Momentum Histogram before Momentum Cuts are Applied 108 4-17. Ty p i c a l S2 to RF TOF Histogram After a l l Cuts .... .. 1 1 0 4-18. Geometry for Determining Scattering Angle 1 H 4-19. Histogram of Calculated Scattering Angles. .................. x i Page 4-20. Pulse Height i n the Total Energy Counter H 7 4-21. ADC Channel vs. Energy - 319 MeV Beam 118 4- 22. ADC Channel vs. Energy - 493 MeV Beam H 9 5- 1. Kinematic Quantities Describing Double Scattering 125 5-2. Neutron Monitor Rate vs. Proton Monitor Rate 132 5-3. V a r i a t i o n of Neutron Signal as a Function of PI to P2 TOF Cut 141 5-4. V a r i a t i o n of Neutron Signal as a Function of the "Carbon" Cut 142 5-5. E f f i c i e n c y vs. 1/T (Kinetic Energy) 145 5-6. Ratio of "Wide Angle" to "In Beam" Neutron Monitor at 319 MeV 147 5-7. Ratio of "Wide Angle" to "In Beam" Neutron Monitor at 493 MeV 148 5-8. V a r i a t i o n of Normalization as a Function of PI to P2 TOF Cut I 6 0 5-9. V a r i a t i o n of Normalization as a Function of "Carbon" Cut ... 161 5-10. D i f f e r e n t i a l Cross Section at 319 MeV 165 5-11. D i f f e r e n t i a l Cross Section at 493 MeV 168 5-12. Legendre Polynomial F i t to D i f f e r e n t i a l Cross Section at 319 MeV 171 5- 13. Legendre Polynomial F i t to D i f f e r e n t i a l Cross Section at 493 MeV 172 6- 1. Schematic of Total Cross Section Experiment 176 6-2. Neutron Detector for Tot a l Cross Section Experiment 179 6-3. Diagram of E l e c t r o n i c Logic for Tot a l Cross- Section Detector 18° x i i Page 6-4. E l e c t r o n i c Logic for To t a l Cross Section Monitor 182 6-5. E l e c t r o n i c Logic for Computer Trigger 183 6-6. F u l l and Empty Rates at 417 MeV as a Function of Time 190 6-7. D i f f e r e n t i a l Cross Section at Zero Degrees as a Function of Energy 194 6- 8. T o t a l Cross Sections vs. Energy 197 7- 1. Previous D i f f e r e n t i a l Cross Section Measurements at Energies near 319 MeV 199 7-2. LAMPF Measurement of the D i f f e r e n t i a l Cross Section at 324.1 MeV 201 7-3. P.P.A. and LAMPF Measurement of the D i f f e r e n t i a l Cross Section near 493 MeV 203 7-4. Saclay Measurement of the D i f f e r e n t i a l Cross Section near 493 MeV 204 7-5. E x i s t i n g T o t a l Cross Section Measurements between 200 and 500 MeV 206 7-6. Precise T o t a l Cross Section Measurements 209 7-7. 3 S 1 , T1 and ^ Phase S h i f t s 214 . — 1 3 7-8. 6.0, F 0 and P Phase S h i f t s 215 3 3 o 7-9. 3 D 1 } 3 D 2 and 3 D 3 Phase S h i f t s 216 7-10. 3G 3, 3 G 4 and 3 G 5 Phase S h i f t s 217 7-11. Central, Spin-Orbit and Tensor Components of the D Phase S h i f t s 219 7-12. Central, Spin-Orbit and Tensor Components of the G Phase S h i f t s 220 x i i i TABLES Page 1-1. Tensors Making Up the Scattering Amplitude 5 1-2. Behavior of Rotation-Invariants Under Space R e f l e c t i o n , Time Reversal and the P a u l i Exclusion P r i n c i p l e ° 1-3. Symmetry Properties of the C o e f f i c i e n t s of the M Matrix Under the Replacement of 6 by Tf _ 0  9 1-4. U n i t a r i t y Conditions f o r the C o e f f i c i e n t s of the M Matrix Below Pion Threshold 1 0 1- 5. Experimental Observables i n Terms of the C o e f f i c i e n t s of the M Matrix 13 2- 1. Dimensions of S c i n t i l l a t o r s i n the Primary Proton Beam Monitor 36 2-2. Neutron Beam Energy 40 2- 3. Dimensions of Elements of the Neutron Beam Monitor 43 3- 1. Dimensions of S c i n t i l l a t o r s i n the LH^ Monitor 55 3- 2. Magnetic F i e l d Map of Momentum Analyzing Magnet 67 4- 1. Signal and H for Neutron Data at 319 and 493 MeV 8 9 4- 2. Error Matrix f o r Cubic F i t to E f f i c i e n c y 9 ± 5- 1. Attenuation and Double Scattering Correction f o r Neutrons .. 124 5-2. D i f f r a c t i o n Scattering Correction f or Neutrons 127 5-3. Correction to Neutron Data f o r I n e l a s t i c Events 127 5-4. Corrected Scattering Angles f o r Neutrons 131 5-5. Attenuation and Double Scattering Corrections f o r Protons -Magnetic Spectrometer 134 5-6. D i f f r a c t i o n Scattering Correction f o r Protons 135 5-7. Scattering Angle Corrections f o r Proton Data 136 5-8. Attenuation and Double Scattering Corrections f o r Protons- -x i v Page Total Energy Spectrometer 138 5-9. Corrections for Interaction T a i l for Tot a l Energy Spectrometer Data 139 5-10. E f f i c i e n c y Ratio and Tot a l S t a t i s t i c a l Error f o r each Lab. Angle at 319 and 493 MeV 144 5-11. Summary of Errors on Neutron Signal 150 5-12. Summary of Angle Independent Errors on Proton Signal 152 5-13. Summary of Errors on Proton Signal. 153 5-14. Summary of Errors on T o t a l Energy Data 156 5-15. Summary of Normalization Errors 158 5-16. D i f f e r e n t i a l Cross Section at 319 MeV 163 5-17. D i f f e r e n t i a l Cross Section at 493 MeV 166 5- 18. C o e f f i c i e n t s of Legendre Polynomial F i t s to D i f f e r e n t i a l Cross Section at 319 and 493 MeV 170 6- 1. Table of Tot a l Cross Sections Calculated from each Consecutive P a i r of Full/Empty Runs 188 6-2. Summary of Tot a l Cross Sections and Neutron Beam Energies .. 189 6-3. Table of Data and the Results of a Linear F i t at 417 MeV ... 192 6-4. Summary of Corrections to Tot a l Cross Section 195 6- 5. Corrected Values of T o t a l Cross Section 196 7- 1. E x i s t i n g n-p Tot a l Cross Section Measurements between 200 and 500 MeV . 207 7-2. C o e f f i c i e n t s of f i t to New Tot a l Cross Section Data plus Data of Kazarinov^ 3, Ashmore^ and Bugg^"**2 208 7-3. C o e f f i c i e n t s of f i t to P.P.A. Tot a l Cross Sections 208 G6 7-4. Results of Dispersion Relation Analysis i n the Inter-mediate Energy Range 211 X V Page 7-5. Real Part of Forward Scattering Amplitude from P.S.A. and Dispersion Relation 212 7-6. Phase S h i f t Analysis of World Data With and Without New Cross Sections 213 1 I. Introduction 1-1. H i s t o r i c a l Background New measurements of the neutron-proton d i f f e r e n t i a l cross section at 319 and 493 MeV and of the t o t a l cross section at 212, 268, 319, 368, 417 and 495 MeV are described i n t h i s t h e s i s . The experimental e l u c i d a t i o n of the two body force between nucleons has been the subject of Ml, HI, Wl a large and long research programme. Nuclei provided the f i r s t experimental data on the "strong force " B l LI that binds nucleons together. ' The binding energy per nucleon nearly 4 saturates at He and i s roughly constant i n larger n u c l e i , i n d i c a t i n g a -15 short range force (approximately 10 m). The s i m i l a r binding energies 3 3 of H and He suggest that the i n t e r a c t i o n i s charge independent. Unfor-tunately there i s only one bound state of the two nucleon system, the deuteron. Therefore a f u l l understanding of the nucleon-nucleon (N-N) i n t e r a c t i o n requires the extra data provided by s c a t t e r i n g experiments. Early, very low energy cross section experiments discovered that the neutron-neutron (n-n) and proton-proton (p-p) s c a t t e r i n g lengths were s i m i l a r . The cross section i s r e l a t e d to the s c a t t e r i n g length by where i s the scattering cross section and & s i s the s c a t t e r i n g length i n the l i m i t of zero energy. Higher energy scattering data at TRIUMF measures the N-N force at the i n t e r a c t i o n distances found i n n u c l e i and at the threshold for pion (fT) production. The N-N i n t e r a c t i o n i s also the study.of the lowest energy baryon-baryon state and therefore i s the prototype p a r t i c l e physics experiment. Scattering experiments provide data that a number of theories try to f i t . Complete sets of accurate N-N s c a t t e r i n g data over a large energy range provide a challenging test f or a v a r i e t y of theories. These include 2 one boson exchange, multiple pion exchange, dispersion r e l a t i o n s and . , S1.M2 p o t e n t i a l s . 1-2. Scattering Formalism Scattering data for two spin h a l f p a r t i c l e s can be parametrized i n a number of e s s e n t i a l l y equivalent ways. A quantum mechanical formalism i s described below. The scattered p a r t i c l e s are written as a superposition of t r a v e l l i n g waves. The sca t t e r i n g of a spin zero beam from a spin zero target i s described at large distances by a function of the form. S y—> oo — ~ y where r i s the distance from the i n t e r a c t i o n point, z i s the component of r along the incident beam axis, k i s proportional to Planck's constant times the momentum of - the scattered p a r t i c l e and f ( r ) i s the scattering amplitude. In t h i s d e s c r i p t i o n the scattered wave i s the remaining unscattered incident plane wave ( e}^^ ) plus an outgoing s p h e r i c a l wave (e. °~ -'/^ T ) with an amplitude f (r) . The s c a t t e r i n g of spin % p a r t i c l e s i s conveniently described by a matrix notation. 1 - 3 T where *)C^ i s a two component spinor representing the incident state and % ^ i s the spinor of the f i n a l scattered state. i s rel a t e d to ")C*U-. by where M i s a matrix of sc a t t e r i n g amplitudes. Each component of M describes the charge, spin and momenta of the scattered p a r t i c l e s . The incident and outgoing momenta of the nueteons in the centre of mass system are 3 denoted by _k and _k' r e s p e c t i v e l y . The unit vectors P_ = (k + l / ) / | l c + lc| , K = (k - |b/|k - k' | and Jfl = (k. x k' ) / |k_ x k'| form a co-ordinate system that i s convenient i n the lab frame. Assuming n o n r e l a t i v i s t i c kinematics, P_ i s the d i r e c t i o n of the outgoing momenta and N i s perpendicular to the scattering plane, (see f £ g u r e 1-1). A l l the tensors up to rank 2 that can be constructed from P_, K, N, O"*'* and C X W . where (y -'* ( Q~ < a ) ) r e f e r s to the spin of the f i r s t (second) nucleon, are l i s t e d i n table 1-1. The most general expression of M, the matrix of s c a t t e r i n g amplitudes, i s a l i n e a r combination of these tensors. However, M i s invariant under c e r t a i n transformations corresponding to conservation laws. The conservation of angular momentum implies the s c a t t e r i n g amplitude i s r o t a t i o n a l l y i n v a r i a n t ; hence, i t i s a scalar or a pseudoscalar. Seventeen possible combinations of the tensors are l i s t e d i n table 1-2. The constraint £ l , W w = a*°-J$ ? l l \ K + cr (0-P g-^-P + o ; ( , > -N a u V y . ± _ 5 leaves 16 independent q u a n t i t i e s . Space r e f l e c t i o n invariance, r e s u l t i n g from the conservation of p a r i t y i n strong i n t e r a c t i o n s implies that the expression f o r the amplitude remains the same under the following transformations: P_—> -P, K—> -K, N—* -N and _0"^,,J'^ > _0^,,1\ Time r e v e r s a l invariance implies the transformations K-*K, N—> -N, P—v-P and CT0'3^ > CT^'X) leave the expressions, for M unchanged. The P a u l i exclusion p r i n c i p l e requires the sc a t t e r i n g amplitude f o r i d e n t i c a l p a r t i c l e s to remain the same i f the labels (1) and (2) are interchanged. Charge independence of the scattering amplitude means the neutrons and protons are treated as i d e n t i c a l p a r t i c l e s and therefore the n-p sc a t t e r i n g formalism i s also subject to t h i s r e s t r i c t i o n . FIGURE 1-1 KINEMATIC DIAGRAM FOR NEUTRON PROTON SCATTERING 5 TABLE 1-1 Tensors making up the Scattering Amplitude Tensors of the Rank Spin Vectors Kinematic Tensors (1) (2) 1 K-P P-N N-K a ( 1 ) + o : ( 2 ) K <r ( 2 ) N < T ( 1 > * a ( 2 ) aP*.™ + cr. (V ( 2 ) K . K . 1 3 j 1 1 J P.P. N.N. 1 J K.P. + K.P. 1 J J 1 K.N. + K.N. 1 J J 1 P.N. + P.N. 1 J J 1 6 TABLE 1-2 Behavior of Rotation Invariants Under Space R e f l e c t i o n , Time Reversal, and the P a u l i Exclusion P r i n c i p l e Y Denotes Invariance N Denotes No Invariance Rotation Space Time Exclusion Invariant R e f l e c t i o n Reversal P r i n c i p l e 1 Y Y Y c r ( 1 ) , < r ( 2 ) Y Y Y a ( 1 W 2 )-K N N Y •N Y Y Y •P N Y Y a ( 1 ) - a ( 2 ) - K N N N •N Y Y N •P N Y N a ( 1 W 2 )-K N Y N •N Y N N •P N N N i j j i Y Y Y N.N. i 3 Y Y Y P.P. i J Y Y Y K.P. + K.P. 1 3 3 1 Y N Y K.N. + K.N. 1 3 3 i N N Y P.N. + P.N. 1 3 3 1 N Y Y 7 A t o t a l of f i v e expressions remain. The s c a t t e r i n g amplitude, a l i n e a r combination of these expressions with c o e f f i c i e n t s that depend on momentum and scattering angle, i s given by + Vi ( k,e ) ( a l 0 - P a ^ . p -al,).Kgu).K) 1 _ 6 The derivation s o f a r treats the nucleons i n the s c a t t e r i n g process as disti n g u i s h a b l e . In p-p sc a t t e r i n g , c l e a r l y i t i s not possible to t e l l the scattered proton from the r e c o i l proton. Hence, the measured quantities must be symmetric about TT /2. This can be extended to n-p sca t t e r i n g as we l l , by considering M as a matrix i n i s o s p i n space. The sca t t e r i n g amplitudes f o r the ph y s i c a l processes can be factored into pure i s o s p i n amplitudes -PP—* PP 1 Mn P->n ? = k (M> + V 1 " 8 1 - 9 where i s the matrix of sca t t e r i n g amplitudes f o r the t o t a l i s o s p i n equal to one (1=1) and M Q i s the 1=0 matrix. The wave function of the scattered nucleons, where *V(r) i s the s p a t i a l wave function, i s the t o t a l spin wave function and i s the t o t a l i s o s p i n wave function, must be a n t i -symmetric with respect to the exchange of the nucleons. This requires H2 ce r t a i n r e l a t i o n s h i p s between the c o e f f i c i e n t s of-the M matrices under the replacement of 0 by If — 6 . These r e l a t i o n s h i p s are l i s t e d i n table 1 - 3 . The previous discussion has been n o n - r e l a t i v i s t i c . I t can be made S2 S3 f u l l y r e l a t i v i s t i c ' with respect to the p o s i t i v e energy states by including the Wigner r o t a t i o n i n the s c a t t e r i n g angle and by applying a Lorertz transformation to theDirac spinors for the nucleon spin states. A good H2 d e s c r i p t i o n of t h i s i s given by Hoshizaki 1-3. Complete Set of Experiments The number of measurements that w i l l determine the s c a t t e r i n g P2 amplitudes has been studied by Puzikov, Ryndin and Smorodinsky and S4 H2 by Schumacher and Bethe and i s described by Hoshizaki Since there are f i v e complex c o e f f i c i e n t s , the minimum number of measure-ments would be nine leaving one a r b i t r a r y o v e r a l l phase. However, the equations are nonlinear and cannot be solved uniquely with nine experiments; i t a c t u a l l y requires I I . Below the pion threshold there i s a u n i t a r i t y condition for each of the c o e f f i c i e n t s - see table 1 - 4 - that i s derived from the u n i t a r i t y of the s c a t t e r i n g matrix : R + R + = - R+ R 1 - 1 1 where S = R + 1 1 - 1 2 and M = aJL < I S - I | p • > 1 - 1 3 i V thus, reducing the number of measurements to 5. If the M matrix i s known, then the M Q matrix can be found with fewer than 5 n-p measurements. Experiments at 6 and TT - Q y i e l d two independent b i t s of information because of the interference between the M 0 and M, amplitudes. Thus, the number of measurements i s 3 (6 ) below (above) pion threshold. 9 TABLE 1-3 Symmetry Properties of the C o e f f i c i e n t s of the M Matrix under the Replacement of © by TT - 0 1 = 1 a(e) - m{6) - - K j d r - e ) c(e) = c(tr-e) Me) = Mrr-e) I = 0 ale) + mle) = a.{Tx-e) + wt (Tr-e) ale) - YrtCe) = ^ l ^ r - e ) h(o) = -K (T r-e ) TABLE 1-4 U n i t a r i t y Conditions for the C o e f f i c i e n t s of the M Matrix Below Pion Threshold ReCc(0) J = i k . \ l T r lM + M ( o : ( 0 + 2 : u ) ) - n U H I « [ j 8 ) ] = j L J i T r l M ^ M ^ a s r ^ - ^ A i l ivTT J H X^ Hqte)-k(©)]=_L\j.Trl M+M^-Ke^-Jl) 11 1-4. Density Matrix Formalism M2 The density matrix formalism is a convenient notation f o r r e l a t i n g the experimental observables to the M matrix and the c o e f f i c i e n t s of the expression f o r M. A ph y s i c a l system i s represented by a set of states I fy.^ that are normalized, ( ¥ ± | ^ ^ =1, but not necessarily orthogonal. The measure-ment of an observable A on a system that i s In one state I "f'j ^  y i e l d s the eigenvalue a f c . The average eigenvalue of an a r b i t r a r y system i n a pure state . { 15<^= S where S ^ = 1 ) i s given by the expectation value -< F U > = < i j f l l 5 „ > . i - u P a r t i c l e beams are most e a s i l y described as a sum of normalized states. This mixed state becomes i _ i \. 1 - 1 5 such that 2^  = 1 , where Is the f r a c t i o n of the state \ "typ y in J . The expectation value i s the weighted mean of the expectation values of the pure states. By i n s e r t i n g a complete set of orthonormal states, 1*3^^ '^ , where \ = S;- and 2 = 1, into equation 1-16 1 - 1 7 and defining a density of state operator to be m 2 12 the expectation value of A i s written i n a very compact notation -< fl> = Tr (pH) . 1 - 1 9 The p o l a r i z a t i o n i s the spin expectation value of a mixed state. It i s denoted by , where br ~ cr. «yp = 0 , 1 , 1 , 3 1 - 2 0 ' 'jJL = 0,l,A ;...j ll 10 _ U ) yx. = O , I 3., .  . j / fe i s the tensor product of the P a u l i matrices for the spin of each nucleon. The unpolarized state i s denoted by which i s equal to the unit matrix. The f i n a l state p o l a r i z a t i o n i s written as 1 - 2 1 where i s the spin-density matrix for the f i n a l state and the denominator, Tr(^ ), i s included to relax the condition that the pure state vectors are normalized. The f i n a l state spin density i s given i n terms of the i n i t i a l state spin density by 1 - 2 2 where i s written i n terms of the I n i t i a l p o l a r i z a t i o n -/>. = 2 x < S f > T r U ) S*" The f i n a l state p o l a r i z a t i o n i s written e n t i r e l y i n terms of the matrix of scattering amplitudes and the i n i t i a l state p o l a r i z a t i o n by i < s r > = i S < S ? > T T ( M S T M V ) 1 - 24 where 13 TABLE 1-5 Experimental Observables i n Terms of the Coe f f i c i e n t s of the M Matrix J a . rE I e f l = -iu»-ivn.1X-HR«^K*)W| +lReli(o,-w)*clcos| XofV= a.Rei»U->nfcl5iilfl +i)a.lx-UIX+ifReUK*)3cose 2 J a. C O S © . I o C K P = If RftlicVi ) 14 dcr dX2 D R A A' R1 PARAMETER SPIN CONFIGURATION FIGURE 1-2 DIFFERENTIAL CROSS SECTION AND POLARIZATION PARAMETER FIGURE 1-3 WOLFENSTEIN POLARIZATION - TRANSFER PARAMETERS 16 X = T r l n ^ M ^ / TV (f>c) 1 - 2 5 or s u b s t i t u t i n g f o r - . • I = S *<S£>TV(MS VM +) The e x p l i c i t formulae- f o r the observables i n terms of the c o e f f i c i e n t s M3 of the M matrix are l i s t e d i n table 1-5 and are given by Moravscik H2 and Hoshizaki 1-5. Experimental Observables The p o s s i b l e experiments i n nucledn-nucleon s c a t t e r i n g include the W2 d i f f e r e n t i a l cross section, the Wolfenstein t r i p l e s c a t t e r i n g parameters and the spin c o r r e l a t i o n s . The d i f f e r e n t i a l cross section i s a measurement of the rate of scattered p a r t i c l e s from an unpolarized beam in-cident'on ah unpolarized target. The Wolfenstein parameters are a measure-ment of the f i n a l state p o l a r i z a t i o n of nucleons scattered from a polarized beam on an unpolarized target. These observables are shown schematically i n f i g u r e 1-2. The Wolfenstein p o l a r i z a t i o n transfer parameters are the same except the f i n a l state p o l a r i z a t i o n of the r e c o i l p a r t i c l e i s measured. These are shown i n f i g u r e 1-3. The second rank ( t h i r d rank) s p i n - c o r r e l a t i o n tensor i s measured by s p e c i f y i n g any two (three) of the p o l a r i z a t i o n s . 1-6. Phase S h i f t Parametrization Alternate parametrizations of the M matrix e x i s t , of these the phase s h i f t representation and phenomenological po t e n t i a l s are the most widely M4 used. The phase s h i f t representation , r e s t r i c t e d to spin zero, is: discussed f i r s t . Experiment and theory are most e a s i l y compared i n t h i s representation. 17 The most general solution.to the Schrodinger equation f o r a s p h e r i c a l l y symmetric p o t e n t i a l Is given By oO *t= 2 flLPLuose> T \ ( - O i - 27 where P^  (cos©) are Legendre polynomials, are constants to be determined and f t (r) are the solutions to the r a d i a l wave equation. At large distances from the s c a t t e r i n g centre the p o t e n t i a l i s zero and the sol u t i o n to the r a d i a l equation f o r no p o t e n t i a l i s j (kr), the s p h e r i c a l Bessel functions. The asymptotic form of j (kr) i s A (kr) > J_ srnAkr - LIT) ± _ 2 8 <U kr — f C o kr 31 which i s the superposition of an outgoing and an incoming s p h e r i c a l wave. The e f f e c t of the p o t e n t i a l i s to s h i f t the r e l a t i v e phase of these waves. Therefore, the asymptotic s o l u t i o n to the r a d i a l wave equation i s of the form T t r ) »• e + l - 29 where i s the sca t t e r i n g matrix f o r the 1th p a r t i a l wave. The only incoming wave i s the incident beam so the c o e f f i c i e n t s A^ are adjusted to match the expansion -e ^ = § U U i V i M . l k O R u o s e ) The amplitude of the outgoing wave i s now i d e n t i f i e d as •Pie) = I U U Q P. icose) (S. - 0 1 - 3 0 1 - 3 1 The s c a t t e r i n g amplitude can be d i r e c t l y r e l a t e d to the d i f f e r e n t i a l cross section. The p r o b a b i l i t y of a scattered p a r t i c l e being at a point ( r , 0 , ^>) i s given by the square of the scattered wave function -18 ITI®)) / T"3* . The number of p a r t i c l e s crossing, an area dA = r a d X L (where d X l i s the s o l i d angle subtended by the area dA,at the sca t t e r i n g centre) per incident p a r t i c l e i s the d i f f e r e n t i a l cross section and i s given by dL<r = I U B ) \ X 1 - 3 2 The t o t a l number of scattered p a r t i c l e s per incident p a r t i c l e i s c a l l e d the t o t a l cross section and i s given by cr = \ do- A i l — o-Tt [\he) \Xs\ne cL 6 1 - 3 3 The t o t a l cross section and the s c a t t e r i n g amplitude are related by the Optical Theorem -C T ^ . — lv1T Imt TC0)D 1 - 3 4 Since the r e a l and Imaginary parts of an a n a l y t i c function are related by the Cauchy i n t e g r a l theorem, the f u l l s c a t t e r i n g amplitude at zero degrees i s derived from a knowledge of the t o t a l cross section as a function of energy. The s c a t t e r i n g matrix i s unitary ( I S^l =1) below pion threshold because the number of p a r t i c l e s and the t o t a l angular momentum are conserved. A convenient way to write a unitary operator i s 1 - 3 5 where i s known as the phase s h i f t f o r the L— p a r t i a l wave. I t i s the dif f e r e n c e i n phase between an unscattered and scattered wave due to the change i n wavelength (momentum) of the p a r t i c l e when i t i s i n the p o t e n t i a l . Introducing r e l a t i v i s t i c kinematics does not change the p a r t i a l 19 wave expansion (equation 1-31) but the onset of i n e l a s t i c reactions breaks the u n i t a r i t y of the sca t t e r i n g matrix. This i s accommodated by wr i t i n g = fa ^  K I O < ^  < 1 ) 1 - 3 6 where yC^ i s the i n e l a s t i c i t y parameter. Spin i s e a s i l y incorporated f o r c e n t r a l p o t e n t i a l s where J , , L and S are a l l conserved. J , the t o t a l angular momentum i s given by J = L, + S. 1 - 3 7 where L_ i s the o r b i t a l angular momentum and S_ i s the t o t a l spin given by S = S, + S_A 1 - 3 8 For each 1 there are three values of J ; these are -t + s, s, -£ — s. The phase s h i f t for each of these states i s denoted by, L» where L = S,P,D,F, for 1 = 0,1,2,3, ... . The nucleon-nucleon i n t e r a c t i o n has a noncentral component and x therefore the o r b i t a l angular momentum L no longer commutes with the Hamiltonian. The conserved quantities i n t h i s i n t e r a c t i o n are the p a r i t y x P, the t o t a l angular momentum and one of i t s components J and and the t o t a l spin S . The possible phases for the 1 = 0 and the 1 = 1 cases are shown i n figu r e 1 - 4 . The P a u l i p r i n c i p l e demands that the t o t a l wave function be antisymmetric with, respect to the exchange of the p a r t i c l e s . Therefore, the t o t a l symmetry of the i s o s p i n , spin and the o r b i t a l angular momentum must be antisymmetric. For example an isovector (I = 1) spin t r i p l e t state (S = 1) must have odd values f o r the o r b i t a l angular momentum. There are three values of -t possible for each value of the t o t a l 20 21 angular momentum greater than zero, "t = J - 1, "C = J and 1 = T + 1. The states with 4, = J + 1 have the same t o t a l angular momentum, spin and p a r i t y and are therefore free to.couple. S T becomes a two by two matrix. The diagonal representation of S5 S 7 given by Stapp i s j S*-h3 O e 1 o 39 where 7 a r e known a s t n e ^ a r Phase s h i f t s and £ y as the bar mixing parameter. The M matrix and the observables may both be written i n terms of phase s h i f t s . The p a r t i c u l a r advantage of t h i s representation i s that f o r short range i n t e r a c t i o n s the contribution to the sc a t t e r i n g amplitude decreases with increasing -t. Sem i c l a s s i c a l l y t h i s i s because large values of "t. correspond to large impact parameters and high energy where the "strong i n t e r a c t i o n " i s weak. The phase s h i f t s can be determined by f i t t i n g very low energy s c a t t e r i n g data with only the t = 0 phases; as the energy i s increased more phase s h i f t s are included. Thus, demanding the phase s h i f t s have a smooth v a r i a t i o n with energy gives a good p r e s c r i p t i o n f o r fi n d i n g a consistent phase s h i f t representation. Phase s h i f t s also provide a convenient means of adding theory to the analysis. The Born approximation r e l a t e s small phase s h i f t s to pote n t i a l s by n OO M where V(r) i s a ce n t r a l p o t e n t i a l . Agreement between a phase s h i f t calculated by theory and by a f i t i s a c r i t e r i o n f o r an acceptable minimum value of •£ for which the phase s h i f t s can be supplied e n t i r e l y by theory. 1 ^ Jo H 1 - 4 0 22 However, the precise value of the phase s h i f t s w i l l depend upon the t h e o r e t i c a l input that was incorporated i n the ana l y s i s . This includes the r e s u l t s of one boson exchange c a l c u l a t i o n s , dispersion i n t e g r a l s and energy parametrizations of the phase s h i f t s . 1-7. Phenomenological Po t e n t i a l s P2 The most general phenomenological p o t e n t i a l that can be con-structed from the momentum, the r e l a t i v e p o s i t i o n vector, the spin and the angular momentum of the nucleons that i s invar i a n t under t r a n s l a t i o n , r o t a t i o n , the r e f l e c t i o n of the s p a t i a l axes and time r e v e r s a l i s given by V = V +V +V cr -cr, +V S + \ L Q 1 - 4 1 where 42 and 1 - 4 3 and 0~i i s the P a u l i spin matrix f o r the 1— nucleon. Each c o e f f i c i e n t i s written as VL=V"lr,?,U + V i V J ? , U % -t*. 1 - 4 4 where i s the i s o s p i n of the i — nucleon. The subscripts c, L.S, CT , fl"L and T denote c e n t r a l , s p i n - o r b i t , spin-spin, quadratic s p i n - o r b i t and tensor. P2 These potentials are adjusted u n t i l they f i t the phase s h i f t s given by experiment. A number of f i t s have been made. The most well known are the Hamada - Johnston and Reid p o t e n t i a l s . L2 R l The most modern approach to t h i s problem i s the Paris p o t e n t i a l 23 The N-N i n t e r a c t i o n i s calculated from one pion exchange, correlated and uncorrelated two pion exchange, one boson exchange, u? exchange and dispersion r e l a t i o n s obtained from TV -N and TT - TV s c a t t e r i n g . This gives good r e s u l t s f or the phase s h i f t s with J> 2 and then a phenomenological f i t i s made for r < .8 fm. The t o t a l number of parameters used i n the f i t i s 6. They are the value of a constant soft core (depth of a square well p o t ential) f o r the c e n t r a l , spin-spin, tensor, s p i n - o r b i t and quar-d r a t i c s p i n - o r b i t components as well as a parameter f o r a l i n e a r energy dependence of the c e n t r a l part. The measurements i n t h i s thesis w i l l be compared with the Paris p o t e n t i a l i n chapter 7. 1-8. Experimental Review A large body of nucleon-nucleon s c a t t e r i n g data e x i s t s and i s , , j . 1. ^ •, B2,W1,H1,A1,A2,01 tabulated xn a number of places The data has A l A2 A3 B3 been used i n phase s h i f t analyses ' ' ' and for determining . - L2 potentxals In the 1940's and 1950's a number of synchrocyclotrons were b u i l t that reached energies of one to several hundred MeV. N-N sc a t t e r i n g measurements were made at new accelerators at Harvard, Harwell, Orsay, Rochester, Liverpool, Chicago, Dubna and Berkeley. Synchrotrons i n the few GeV range at Saclay, Princeton, Berkeley, Argonne and others followed soon a f t e r . The p-p sc a t t e r i n g parameters were measured - ° T : O T » d t r / d - Q . , P, D, R, A and C ^ . However the Wolfenstein parameters were very d i f f i -c u l t to measure as they required three scatters f o r each event. Very few n-p s c a t t e r i n g measurements were attempted as a neutron beam had to be produced by yet another s c a t t e r i n g . Measurements were made of the t o t a l and d i f f e r e n t i a l cross section and p o l a r i z a t i o n . A series of measurements were made with protons on deuterium. However, a d i f f i c u l t c o r r e c t i o n was 24 necessary to account f o r the neutron being shadowed by the proton. As a r e s u l t the p-p (I = 1) phase s h i f t s were uniquely determined up to B4 600 MeV . I t was noted however, that a few measurements i n angular ranges where data was sparse would greatly reduce the errors on the computed phase s h i f t s . The- n-p system was not uniquely determined. A comprehensive programme of n-p t r i p l e s c a ttering measurements and cross sections was needed to f i x the 1 = 0 p h a s e s ^ . Two important experimental development occurred that enabled N-N sc a t t e r i n g experiments to be performed with high p r e c i s i o n : meson f a c t o r i e s and multiwire proportional chambers. The high i n t e n s i t y , v a r i a b l e energy, well-focussed beams av a i l a b l e at TRIUMF between 180 and 518 MeV are i d e a l f o r N-N s c a t t e r i n g . CI Multiwire proportional chambers (MWPC) provide a detector that can be b u i l t large but with good s p a t i a l r e s o l u t i o n and f a s t enough to take the data c o l l e c t i o n rates necessary i n high s t a t i s t i c s experiments. The output of these detectors i s e a s i l y interfaced to the on-line computers t y p i c a l l y used for data a c q u i s i t i o n . 1-9. BASQUE Programme to Determine the 1=0 Phase S h i f t s B14 The BASQUE group have been involved i n a programme to measure the N-N s c a t t e r i n g amplitude through unique and precise determinations of the 1=0 phase s h i f t s . Since t h i s requires both n-p and p-p data, the P, D, R and R' p a r a m e t e r s ^ 4 ' ^ ^ w e r e measured i n the p-p system and a double sc a t t e r i n g experiment was performed to determine the absolute normali-* i . . . A5,KI zatxon of the p-p p o l a r i z a t i o n The BASQUE n-p s c a t t e r i n g measurements were divided into three sections P and D ^ , R and A ^ and the subject of t h i s thesis o^ O T t ' t t J 0 1 and do- /dSL . The measurement of der /dXlwas absolutely normalized over the e n t i r e angular range. 25 The d i f f e r e n t i a l cross section f i x e s the c e n t r a l part of the N-N p o t e n t i a l . The BASQUE t r i p l e s c a t t e r i n g parameters fixed the spin dependent components of the p o t e n t i a l such that there was a smooth B 7 v a r i a t i o n of the phase s h i f t s with energy . The normalization of the d i f f e r e n t i a l cross section provides the normalization for a l l of the N-N observables (see table 1-5) and therefore has a strong e f f e c t on the phase s h i f t a n a l y sis. The phase s h i f t solutions are s e n s i t i v e to the spin-average forward s c a t t e r i n g amplitude; e s p e c i a l l y at 325 MeV where there are two solutions, R7 one with f(Q) free the other with, i t constrained. The forward s c a t t e r i n g amplitude can be calculated from a dispersion r e l a t i o n i f the t o t a l cross section i s known at a l l energies. The energy v a r i a t i o n of 0~TOT was previously not c l e a r i n the intermediate energy range and new measurements described i n t h i s t hesis have improved t h i s . The t o t a l cross sections were measured at 212, 268, 319., 368, 417 and 495 MeV by a transmission experiment. The t o t a l number of p a r t i c l e s scattered from a beam neglecting double s c a t t e r i n g i s r e l a t e d to the cross section by where n t i s the number of protons per unit area i n the target and n i « v T (n f ) are the number of neutrons detected without (with) the hydrogen target i n the beam per neutron monitored upstream of the target. The 1% to 3% p r e c i s i o n measurements- of the t o t a l cross section show a smooth energy v a r i a t i o n . Precise measurements of the d i f f e r e n t i a l cross section were made at 319 and 493 MeV. Data was c o l l e c t e d over the f u l l angular range, 0 to 180 degrees, with an absolute normalization, by measuring both scattered 1-10. The Cross Section Measurements cr. 1 - 4 5 26 neutron and proton rates with c r o s s - c a l i b r a t e d detectors and monitors. The uncertainty i n the normalization was 2.8% at 319 MeV and 3.7% at 493 MeV. The normalization was checked by comparing the overlap of the neutron and proton data and by the constraint provided by the t o t a l cross section -Cr - <r + I'TC V a-cr S»n»© d © 1 - 4 6 T O T \HS.LftS"MC J The d i f f e r e n t i a l cross section i s the number of p a r t i c l e s detected per unit s o l i d angle, per incident p a r t i c l e , per target p a r t i c l e at a s p h e r i c a l polar angle & . This i s written as d-CT = tics d.-Q.L*E. 1 - 4 7 where n Q i s the number of p a r t i c l e s detected, n t i s the number of target p a r t i c l e s per unit area, A-Q. i s the s o l i d angle subtended by the detector and d j f l ^^ /d.CL* i s the Jacobian.that transforms the s o l i d angle from the lab to the centre of mass. As i t i s impossible to detect a neutron without removing i t from the beam, the value of n ^ cannot be determined d i r e c t l y . Instead the neutron beam was monitored by sampling a f r a c t i o n of the incident p a r t i c l e s upstream of the s c a t t e r i n g target. The neutron detector was placed at 0°, i . e . i n the beam, and the r a t i o of the number of detected to monitored neutrons was measured. However, the neutron detector e f f i c i e n c y was energy dependent and the energy of the neutrons incident on the detector was a function of s c a t t e r i n g angle. Denoting the e f f i c i e n c y as a function of k i n e t i c energy by (T) , the d i f f e r e n t i a l cross section becomes 27 Atr = YID jLiluoc r^lTlo*)) I - 48 A i l * YXtKiAi l Ailc.M. ^ l T ( e ) ) when n „ i s the number of p a r t i c l e s detected at an angle 8 per monitor count and n-k i s the number of p a r t i c l e s detected at zero degrees per monitor count. The d i f f e r e n t i a l cross section depends only on the r a t i o of the e f f i c i e n c i e s . An associated p a r t i c l e experiment was performed to measure the D2 absolute e f f i c i e n c y . The experiment measured the number of r e c o i l pro-tons and the number of neutrons In coincidence with a r e c o i l proton. Since protons were detected with. 100% e f f i c i e n c y , the r a t i o of coincidences to singles gives the neutron detector e f f i c i e n c y . The experiment was done at f i v e energies. Neutrons cannot be detected much, beyond 45 degrees lab or 90 degrees centre of mass (CM.) as the e f f i c i e n c y of the neutron detector becomes too low. It i s p r e c i s e l y these neutrons that have the most energetic r e c o i l protons. Thus, the remainder of the d i s t r i b u t i o n , 9.0 to 180 degrees CM., can be measured by detecting the protons, but the normali-zation cannot be found by moving the detector to zero degrees. The absolute e f f i c i e n c y of the neutron detector i s used to normalize the proton data. The r a t i o of the number of monitor to detector counts was measured with the neutron detector at zero degrees. Thus, the number of monitor counts per incident neutron i s given by -IMX = Ylj. / Y ^ T l O 0 ) ) 1 _ 49 The expression f o r the d i f f e r e n t i a l cross section, calculated from proton data, i s der ~ TLQ n lT(o")) A-QuflB i _ 5 0 A i l T l t T l ; A X L A - Q _ * 28 The normalization for t h i s measurement i s given e x p l i c i t l y and i s absolute. 1-11. Previous Normalization Techniques Other techniques have been used to normalize n-p d i f f e r e n t i a l cross sections. Measurements over the whole angular range made below the pion threshold were normalized by in t e g r a t i n g the d i f f e r e n t i a l cross section and adjusting the normalization to agree with the measured value of the t o t a l cross section. Measurements of only the change exchange reaction were normalized i n two ways.^ 7'^ Below pion threshold an a r b i t r a r y angle was chosen and the cross section at that angle was plotted as a function of energy. The data plotted were measurements over the e n t i r e angular range that were normalized to the t o t a l cross section. Above the pion threshold the reaction np * TT°d 1 - 5 1 Is used. If the deuterons were detected then the number of incident neutrons could be deduced from the reaction -pp *> Tf+d 1 - 5 2 Reaction 1-52, known experimentally with a p r e c i s i o n of 5% to 7%, produces twice as many deuterons per incident p a r t i c l e as reaction 1-51 i f i s o s p i n Is p e r f e c t l y conserved. 1-12. Organization of Thesis The remaining chapters of t h i s thesis describe the d e t a i l s of the d i f f e r e n t i a l and t o t a l cross section experiments. Chapter two discusses the neutron scattering f a c i l i t y . This i s the apparatus that produces and collimates the neutron beam. The c h a r a c t e r i s t i c s of the cyclotron, primary proton beam, l i q u i d deuterium target (LD^), c o l l i m a t o r s , monitors,sweep magnet and l i q u i d hydrogen (LH^) s c a t t e r i n g target are described. 29 The t h i r d chapter i s about the measurement of the d i f f e r e n t i a l cross section. I t i s i n the following two parts: the neutron detection and the proton measurements. In part one the neutron detector i s described i n d e t a i l . The el e c t r o n i c s and the computer t r i g g e r are outlined. The online computer data a c q u i s i t i o n system i s discussed. A d e s c r i p t i o n of the data taking procedure i s given. Part two follows exactly the same out l i n e but the proton detectors - magnetic and t o t a l energy spectrometers - are discussed. The next chapter i s about the analysis. Again i t i s broken up into two parts; the f i r s t describes the analysis of the neutron events and the second describes the proton a n a l y s i s . The computer codes that f i t t e d tracks, made cuts and f i n a l l y calculated the d i f f e r e n t i a l cross section are explained. Chapter f i v e discusses corrections to the d i f f e r e n t i a l cross section due to known systematic e f f e c t s and i t describes the error analysis. Possible sources of systematic errors are studied q u a n t i t a t i v e l y . The f i n a l r e s u l t s f o r do* /d£L at 319 MeV and 493 MeV are presented. The t o t a l cross section measurement i s the subject of chapter s i x . The p r i n c i p l e s of the experimental procedure are explained, the d e t a i l s of the apparatus are given and the analysis i s discussed. The f i n a l r e s u l t s are described along with an error a n a l y s i s . The d i f f e r e n t i a l and t o t a l cross sections are compared to previous world data i n chapter s i x . A phase s h i f t analysis Is given that serves as a convenient way of studying the e f f e c t of the data on the present experimental understanding of the nucleon-nucleon i n t e r a c t i o n . The energy dependence of the phase s h i f t s Is discussed and a comparison with the Paris p o t e n t i a l i s made. The r e s u l t s and conclusions of t h i s thesis are .then summarized. 31 I I . Neutron Scattering F a c i l i t y A well-collimated intense neutron beam was produced at TRIUMF f o r neutron-proton scattering experiments. Apparatus used i n t h i s f a c i l i t y i s described below i n an upstream to downstream order ( i . e . following the beam d i r e c t i o n ) . The s p e c i f i c detectors and t h e i r arrangement w i l l be explained i n chapters I I I and VI dealing with experiments. I I - l . Cyclotron The TRIUMF cyclotron acclerates H~ ions up to an energy of 520 MeV. One hundred jx. A beams with a beam spot of a few square millimeters i n area are achieved by s t r i p p i n g electrons from the H~ ions at a chosen radius. The allowable range of r a d i i f o r the s t r i p p e r f o i l s corresponds to energies between 183 and 520 MeV. The macroscopic duty factor i s 100% and the normal microstructure i s a 2 to 4 ns long beam burst every 43 ns. As the RF i s the f i f t h harmonic of the cyclotron frequency, f i v e beam "buckets" c i r c u l a t e i n the machine. By i n j e c t i n g only on the f i f t h RF cyc l e , a sin g l e bucket i s accelerated and the microstructure becomes a beam burst every 215 ns. The accelerator RF i s used to stop time to d i g i t a l convertors (TDC) started by detected neutrons. The time between the detection of the neutron and the s t a r t of the next RF pulse i s rel a t e d to the neutron time of f i g h t (TOF) and therefore to i t s energy. This method of energy determination i s ambiguous for low energy neutrons as they may take more than one RF period to reach the detector. This e f f e c t i s eliminated using the 215 ns beam structure. IT-2. Beam Line The beam was transported from the cyclotron by a serie s of quadrupole and dipole magnets, shown schematically i n f i g u r e 2-1. The beam spot was approximately c i r c u l a r with a diameter of 3 to 5 mm at the primary proton 32 FIGURE 2-1 PROTON AREA AND BEAM TRANSPORT 33 beam monitor and at the l i q u i d deuterium target. The proton beam was tuned at low current with the aid of in s e r t a b l e wire chamber monitors to v e r i f y that i t was centred on the l i q u i d deuterium neutron production target. The beam was aligned so that the quadrupole magnets did not steer i t . Proton currents used f o r t h i s experiment ranged from 1 to 500 nA. Non-interacting protons were dumped i n a we l l shielded external dump rated to 10 y. A. II-3. Primary Proton Beam Monitor The proton f l u x incident on the l i q u i d deuterium target was measured by the primary beam monitor. This device L' 3'^ ± consisted of a 12.5 m CH^ f o i l viewed by four p l a s t i c s c i n t i l l a t o r double counter telescopes. The telescopes were mounted i n p a i r s i n the h o r i z o n t a l plane. Each p a i r detected, i n coincidence, a scattered proton at 26° and the r e c o i l proton at 62° corresponding to the kinematics f o r e l a s t i c proton-proton s c a t t e r i n g i n the f o i l . Figure 2-2 shows a schematic of the monitor and indicates the nomenclature used to r e f e r to the s c i n t i l l a t o r s . Each telescope had two counters denoted 1 and 2. Telescopes used to detect forward s c a t t e r i n g protons are designated by an F, r e c o i l telescopes by an R. Looking downstream, the forward telescope on the l e f t (right) of the beam and i t s complementary r e c o i l telescope on the ri g h t ( l e f t ) are denoted L(R). Table 2-1 l i s t s the dimensions of the s c i n t i l l a t o r s . The l o g i c f o r the e l e c t r o n i c s i s shown i n figu r e 2-3. The c h a r a c t e r i s t i c s B6 L3 01 of t h i s monitor have been described i n previous publications ' ' The sum of the monitor counts, L + R, i s proportional to the incident proton f l u x while the asymmetry (L - R)/(L + R) indicates misalignment of the unpolarized beam. 34 PRIMARY BEAM MONITOR BEAM LR telescope Scintillator Notation Ist letter 2 n d letter Number L left F front 1 front R right R recoil 2 back FIGURE 2-2 SCHEMATIC OF PRIMARY PROTON BEAM MONITOR FIGURE 2-3 ELECTRONIC LOGIC DIAGRAM for Proton Beam Monitor i 1 t J L J 1 i S C A L E R S C A L E R S C A L E R S C A L E R S C A L E R TABLE 2-1 Dimensions of S c i n t i l l a t o r s i n the Primary Proton Beam Monitor S c i n t i l l a t o r F l F2 Rl R2 Height mm 30 30 50 70 Width mm 40 50 50 100 Thickness mm 3.2 3.2 3.2 3.2 37 II-4. Liquid Deuterium Target The neutron beam was produced by the d(p, n)2p reaction at 0° . B8 B9 Measurements by Bjork ' v e r i f y the suggestion by Gluckstern and Gl Bethe that the energy spectrum of the neutrons i s sharply peaked. A sample spectrum i s i l l u s t r a t e d i n f i g u r e 2-4. The measured rate of neutrons was approximately 900 per second per nA. H3 The target , shown i n f i g u r e 2-5, consisted of a c y l i n d r i c a l s t a i n l e s s s t e e l f l a s k 200 mm long and 50 mm In diameter, f i l l e d with l i q u i d deuterium. The f l a s k walls were 0.250 mm thick and the end windows 0.050 mm thick. The target assembly was separated from the beam l i n e vacuum by 0.120 mm s t a i n l e s s s t e e l windows. The deuterium was l i q u i f i e d and r e f r i g e r a t e d by a P h i l l i p s A-20 cryogenerator. The maximum power of the A-20 l i m i t e d the proton beam current to 500 nA. The average energy of the neutron peak i s estimated from the energy of the incident proton, the stopping power of the target materials, the deuteron binding energy, the deuteron fermi momentum and the diproton B8 f i n a l state i n t e r a c t i o n . The values f o r these e f f e c t s are l i s t e d In table 2-2 for the primary beam energies used i n these experiments. The neutron beam energies are therefore 319_ and 493 MeV f o r the d i f f e r e n t i a l cross section and 212, 268, 319, 369, 417 and 495 MeV f o r the t o t a l cross section. II-5. 4AB2 Dipole Magnet Immediately downstream of the l i q u i d deuterium target- a dipole magnet was used to bend the unscattered protons through 35 . High energy protons were thus removed from the neutron beam and directed through the remaining beam transport system to a well-shielded external dump. COUNTS FIGURE 2-4 PI TO RF TOF 1200 40d SLOW NEUTRONS r MONOENERGETIC NEUTRONS y RAYS 18 I — I ONE METRE FIGURE 2-5 LIQUID DEUTERIUM TARGET •40 TABLE 2-2 Neutron Beam Energy Energy i n MeV Proton Beam Energy - 505 428 380 331 280 225 Energy Loss i n Target Flask - .23 .27 .29 .31 .34 .38 Energy Loss i n LT>2 - 4.59 5.19 5.44 5.87 6.29 7.31 Deuteron Binding Energy - 2.2 2.2 2.2 2.2 2.2 2.2 Fermi Momentum and F i n a l - 3.25 3.25 3.25 3.25 3.25 3.25 State Interaction Neutron Beam Energy - 495 417 369 319 268 212 41 II-6. Neutron Collimator A neutron beam with a c i r c u l a r cross section was defined by a lead and s t e e l collimator. The collimator was constructed from two load bearing s t e e l p l a t e s , 50 mm thick, with lead sandwiched between them. There were 11 beam ports, spaced from -3° to + 27° i n 3° i n t e r v a l s . Each port was 3.5 m long and was divided i n t o two equal lengths. The upstream portion was 102 mm i n diameter and the downstream part was 127 mm i n diameter. The neutron beam was extracted through the 0° port while a l l other ports were f i l l e d with s t e e l plugs. Figure 2-6 i s a schematic representation of the neutron collimator. The apertures i n the 0° port were defined by d r i l l e d s t e e l plugs. The upstream diameter was 25.4 mm and the downstream diameter was 38.1 mm. The neutron beam was l i m i t e d i n diameter by the 25.4 mm aperture at the centre of the collimator. The downstream h a l f of the collimator was not used to define the f i n a l aperture. Instead, i t further attenuated neutrons transmitted through the upstream material that scattered from the collimator walls. The end of the f i r s t collimator was thus prevented from acting as a source of scattered neutrons. II-7. Neutron Beam Monitors Following the collimator a veto s c i n t i l l a t o r , denoted CV, was used to ensure that charged p a r t i c l e s were not counted i n the monitor. A 25.4 mm t h i c k piece of CH^ converted a f r a c t i o n of the incident neutrons Into charged p a r t i c l e s . The dimensions of the CI^ and s c i n t i l l a t o r are given i n table 2-3. The monitors consisted of telescopes that detected charged p a r t i c l e s from the convertor. A schematic representation "is given i n f i g u r e 2-7. The "In Beam Monitor" consisted of two s c i n t i l l a t o r s , denoted Gl and G2, mounted along the beam axis. The "Wide Angle Monitor" was formed by two FIGURE 2.6 SCHEMATIC OF NEUTRON COLLIMATOR SYSTEM 20! 10 cm 0 -10 -20' STEEL \ \ N N. A \ \ \ \ V / / ; / / / / / / / \ \ 2.873 m I LEAD UCLA MAGNET VACCUUM VESSEL BRASS LIMIT OF MAIN BEAM LH. LIMIT OF UPSTREAM SCATTERS 8.4 cm LIMIT OF ..... j DOWNSTREAM SCATTERS 11.6 cm 9.570 m C_ LH 2 4.2 cm t 15.07 m 10 14 METERS TABLE 2-3 Dimensions o: S c i n t i l l a t o r CV CL1 CL2 CR1 CR2 Gl G2 CH 2 Cu 319 Mev Cu 493 MeV Elements o Height mm 250 200 150 200 150 250 250 226 229 229 the Neutron Width mm 250 210 157 210 157 250 250 237 229 229 Monitor Thickness mm 3.2 1.6 1.6 1.6 1.6 3.2 3.2 25.4 9.5 19.1 FIGURE 2-7 NEUTRON BEAM MONITORS G telescope G 2 Y NEUTRON BEAM 45 double counter telescopes, CL and CR, set up i n the h o r i z o n t a l plane at +29° to the beam axis. The dimensions of the s c i n t i l l a t i o n counters f o r these two monitors are given i n table 2-3 and the l o g i c for the el e c t r o n -i c s i s given i n f i g u r e 2.8. Between the counters i n the Wide Angle Monitor telescopes, 6.3 mm of copper at 319 MeV and 13 mm of copper at 493 MeV ranged out counts from low energy background neutrons. II-8. Sweep Magnet A dipole m a g n e t 1 , 3 , o r i g i n a l l y part of a proton cyclotron at UCLA, was used to sweep charged p a r t i c l e s from the neutron beam that were created i n the monitors and i n the collimator walls. The i n t e g r a l of 13.ell was 5.8 x 10 TmA and t y p i c a l l y the magnet current was 1500A. The magnetic f i e l d was oriented to d i r e c t p o s i t i v e l y charged p a r t i c l e s away from the detectors. II-9. Shadow Collimator The shadow collimator situated i n s i d e the sweep magnet consisted of two aluminium boxes f i l l e d with lead shot and a port made of s t a i n l e s s s t e e l pipe, 0.457 m long, with an insi d e diameter of 51 mm and an outside diameter of 76 mm. A schematic representation i s shown i n figure 2-4. The larger lead box shown i n the diagram shielded the detection apparatus from collimator scattered neutrons. The lead s h i e l d i n g on the opposite side of the beam was cut back so as not to intercept the p o s i t i v e l y charged p a r t i c l e s swept out of the beam by the magnetic f i e l d . As shown schema-t i c a l l y i n f i g u r e 2-6, the shadow collimator did not block any of the main beam. The shadow collimator was positioned to attenuate the neutron flux scattered from the upstream h a l f of the main collimator. Calculations, shown on the schematic as l i m i t i n g case l i n e s , predicted the beam p r o f i l e at the neutron detector p o s i t i o n to be +42 mm wide at the peak, +84 mm. at the base and to have a halo extending out to +116 mm. The measured 46 FIGURE 2-8 ELECTRONIC LOGIC FOR NEUTRON MONITORS f S C A L E R T G2 ) J ^ S C A L E R cv <DELAY <2l5ns S C A L E R t S C A L E R GI-G2J G-CV S C A L E R i f 6-CV CLI \ CL2 C R I CR2 S C A L E R ?' ¥ SCALER 1 S C A L E R " S C A L E R — » r-'r CL-CV CR-CV S C A L E R i D E L A Y [ 215ns S C A L E R S C A L E R 1 1 G-CV-CV 11 (CL4 CR)-CV S C A L E R (CL+CR)-CV-CV S C A L E R S C A L E R 47 beam p r o f i l e shown i n f i g u r e 2-9 i s i n very good agreement with the predictions. 11-10. Liquid Hydrogen Target The l i q u i d hydrogen s c a t t e r i n g target, drawn i n f i g u r e 2-10, con-s i s t e d of a mylar f l a s k 0.39 mm t h i c k , 198.5 mm i n length (which i s equivalent to a 2 to 3% attenuation of the neutron beam) and 136.5 mm i n diameter. The f l a s k was supported s o l e l y at the upstream end by a brass r i n g . Surrounding the f l a s k f o r the l i q u i d was another 0.39 mm thick mylar container that was f i l l e d with hydrogen gas i n pressure equilibrium with the l i q u i d . This prevented bowing of the end windows of the f u l l target f l a s k . The e n t i r e assembly was wrapped i n 10 sheets of aluminized mylar each 9.8 jx. m. The vacuum vessel consisted of two parts, an aluminium housing upstream of the brass support r i n g with a double layer of 0.39 mm thick mylar for the vacuum window, and a 0.13 mm thick aluminium dome on the downstream end. Nucleon absorption and r e c o i l proton multiple s c a t t e r i n g due to the dome were approximately uniform over the target length. The beam diameter extrapolated back to the centre of the scattering target, using the beam p r o f i l e at the neutron detector and the collimator geometry, was 53 mm f o r the main beam and 97 mm for the halo. Therefore the neutron beam did not s t r i k e any of the target f l a s k side walls or supports. The target was maintained at a pressure of 117 + 1.7 kPa (17 + 0.25 PSIA) by a feedback loop from a pressure sensor to the r e f r i g e r a t o r . Liquid hydrogen i n equilibrium with I t s vapour at t h i s pressure has a TI temperature of 20.76 + .06 K . To ensure that the target density did S 6 S 7 not depend on the f r a c t i o n of para-hydrogen, a ca t a l y s t ' was used to convert a l l of the hydrogen to para-hydrogen. 48 FIGURE 2-9 NEUTRON BEAM PROFILE i 1 1 1 1 _l I I 1 L. -300 -100 0 100 mm 300 FIGURE 2-10 LIQUID HYDROGEN TARGET 50 The target could be emptied i n 10 minutes for background measurements and r e f i l l e d i n less than 2 minutes. 11-11. Multiwire Proportional Chambers The wire chambers, e x c e l l e n t l y described i n references W3 L3 and 01, were of two sizes,0.5 m and 1.0 m square. Both had 2 mm sense wire spacing. As the wires were connected In pa i r s to the readout system, an adequate r e s o l u t i o n of 4 mm resulted. Each chamber consisted of a sense wire plane constructed from 20 j£ m diameter gold plated tungsten wire under 50 g tension. Sandwiching the sense plane were two high voltage cathode wire planes. Made of 120 jym diameter copper-beryllium wire strung with a 2 mm spacing and under 100 g tension, they were aligned orthogonal to the sense wires, and had an interplane gap of 8 mm. The wires were encased i n a 0.1 mm thick mylar S9 gas envelope. The Charpak magic gas mixture of argon, freon 13B1, isobutane and methylal was used. W4 The wire readout system , when triggered, recorded each wire that f i r e d and delivered i t s address to the CAMAC output l i n e s as a 24 b i t binary number; the readout time averaged about 2 yu. s per wire f i r e d . 11-12. Helium Bags Two helium bags were used to reduce the amount of material i n the neutron beam. The f i r s t bag was located between the upstream end of the shadow collimator and the upstream end of the l i q u i d hydrogen target vacuum box. It was constructed from 0.15 mm CH a . The second helium bag started at the downstream end of the l i q u i d hydrogen target and ended at the back w a l l of the experimental area. The length was 5.5 m, the diameter 510 mm and the walls were 0.25 mm t h i c k mylar. End windows were 76 t h i c k CH a . The beam losses with the helium bags were estimated from the nuclear 51 K2 c o l l i s i o n lengths to be 20% of the no helium bag case. 52 I I I . D i f f e r e n t i a l Cross Section Experiments Di f f e r e n t experimental techniques were used i n the forward and backward regions of the d i f f e r e n t i a l cross sections. Neutrons were detected for sc a t t e r i n g angles less than 100 degrees i n the CM. whereas r e c o i l protons were detected for centre of mass angles greater than 45 degrees. The o v e r a l l layout of the detection apparatus and the monitors as well as d e t a i l s of the detector, the t r i g g e r and the online data c o l l e c t i o n are described i n t h i s chapter. Neutron detection measurements are taken up i n the f i r s t s ection, the r e c o i l proton experiment i n the second. I I I - l . D i f f e r e n t i a l Cross Section Measured by Detecting Neutrons The neutron detector used to measure the scattered f l u x from the l i q u i d hydrogen target i s represented schematically i n f i g u r e 3-1. A 1.1 m square veto hodoscope for eliminating charged p a r t i c l e t r i g g e r s , l a b e l l e d PV, was composed of eight overlapping s c i n t i l l a t o r s . Figure 3-2 i l l u s t r a t e s the hodoscope, and the counter nomenclature. Downstream of PV, a 1.0 m square wire chamber was used as an o f f - l i n e veto to remove neutrons that converted i n PV but were not detected there. A f r a c t i o n of the neutrons converted Into charged p a r t i c l e s i n a 90 mm thick, 530 mm square block of carbon. The s c a t t e r i n g angle subtended by the carbon was 5.45°. Immediately downstream was a large s c i n t i l l a t o r , 50 mm square and 6,4 mm t h i c k , denoted PI. The counter was viewed from two ends by photomultipller tubes for good l i g h t c o l l e c t i o n e f f i c i e n c y and time r e s o l u t i o n . Downstream of PI, a s e r i e s of seven multiwire proportional chambers were used to measure X^, Y^, X^, Y^, X Q, Y Q and Y, co-ordinates where "X" r e f e r s to h o r i z o n t a l co-ordinates and N E U T R O N D E T E C T O R MWPC 2 (x) MWPC 4 (X) MWPC 6 (x) MWPC 8 (J) NEUTRONS V//////////A F I G U R E 3-1 PV MWPC I (y) VETO CARBON CONVERTER PI MWPC 3 (y) MWPC 5(y) MWPC 7 ( y ) ALUMINUM SHEET P2 SCHEMATIC O F A P P A R A T U S U S E D TO M E A S U R E S C A T T E R E D NEUTRONS 54 F I G U R E - 3 2 P V , P 2 A N D S 3 H O D O S C O P E TABLE 3-1 Dimensions of S c i n t i l l a t o r s i n the LH^ Monitor Height Width Thickness S c i n t i l l a t o r mm mm mm Z l 57 57 3.2 Z2 102 102 1.6 Z3 57 57 3.2 56 "Y" to v e r t i c a l . The chambers were a l l 1.0 m square and had a 4 mm r e s o l u t i o n as described i n chapter I I . The chambers were followed by a 13 mm thick sheet of aluminum and a f i n a l 1.1 m square hodoscope referred to as P2 and i d e n t i c a l to the PV array described above and shown i n f i g u r e 3-2. The t o t a l thickness of material i n the detector f o r an average t r a j e c t o r y was equivalent to the range of 100 MeV protons. The incident neutron f l u x , beam p o s i t i o n and target s t a b i l i t y were observed with three monitors. The incident proton beam monitor was described i n section II-3 and the incident neutron beam monitor was described in~"II-7. Figures 2-2 and 2-5 show schematic representations of the monitors and figures 2-3 and 2-6 indicate the e l e c t r o n i c l o g i c used. S t a b i l i t y of the density of the l i q u i d hydrogen s c a t t e r i n g target was monitored by three colinear counters (a telescope) which detected r e c o i l protons at 45 degrees lab. S c i n t i l l a t o r dimensions are given i n table 3-1. The nomenclature used i s Z l , Z2 and Z3 for the elements of the telescope and Z for the t h r e e - f o l d e l e c t r o n i c coincidence. A l l s c i n t i l l a t i o n counters on the detector and on the monitors were operated on voltage plateaus that were checked before each data taking period. Voltages were c o n t r o l l e d to + 1. v o l t using a LeCroy model HV4032 power supply. The e l e c t r o n i c l o g i c f or the neutron array i s i l l u s t r a t e d i n f i g u r e 3-3. A p o t e n t i a l neutron event corresponded to a PV-P1'P2 e l e c t r o n i c coincidence where PV r e f e r s to no veto counters f i r i n g , PI i s the coincidence between the two tubes viewing the PI counter and P2 i s a s i g n a l i n one or more of the counters from the P2 hodoscope. The coincidence PV«P1-P2, known as the computer t r i g g e r , i n i t i a t e d 57 FIGURE 3-3 NEUTRON DETECTOR ELECTRONIC LOGIC P V A P V B P V C P V D P V E P V F PVG P V H latch latch • / latch , / , latch , / latch / latch • / latch 7 latch A A D C P V P IA S ignal A A D C P I A top r T D S tla tch S C A L E la tch P 2 A P 2 B P 2 C P 2 D P 2 E P 2 F P 2 6 P 2 H ?.R R R 7 7 latch latch latch latch latch D 7 ? 7¥. latch 7 l a t c h S C A L E P I P 2 P V " N E U T R O N S " t Y PIB S i gna l P I B P I V ^ T D C » \ . S top l a t ch P I A + . P I B , S C A L E j S C A L E T D C Start PI P2- PV ' P R O T O N S " S C A L E latch Computer Trigger S C A L E J O the recording of the e l e c t r o n i c data by the on-line computer. In figu r e 3-4 the e l e c t r o n i c l o g i c f o r the computer t r i g g e r i s shown. An event coincidence GAMAC system generated a LAM i n the E.G. and G. C212 coin-cidence buffer that i n i t i a t e d the following data a c q u i s i t i o n cycle i n the computer: 1) A busy s i g n a l was generated and maintained while the computer was reading data. 2) The t r i g g e r l o g i c strobed the latches freezing the b i t pattern (an array of b i t s each i n d i c a t i n g whether or not a s c i n t i l l a t o r had fi r e d ) at the time of the event. 3) The busy s i g n a l gated o f f new events from the s c a l e r s , the time to d i g i t a l convertors (TDC) and the analogue to d i g i t a l convertors (ADC). 4) It triggered the wire chambers, s e t t i n g a f l i p - f l o p on each wire that had f i r e d and started the encoding of the addresses of the wires. 5) A "busy c l e a r " s i g n a l was generated a f t e r a l l of the data was read readying the data c o l l e c t i o n program to take a new event. The on-line computer, a PDP 11/34, read the following information from the CAMAC i n t e r f a c e : 1) The C212 coincidence bu f f e r i n d i c a t i n g the s c i n t i l l a t o r s that had f i r e d . 2) Six scalers . PV-P1-P2, PV-P1-P2, (CL + CR) • CV, G-CV, the l i v e time and the r e a l time. Respectively these are: the numbers to date of neutron t r i g g e r s , proton t r i g g e r s , Wide Angle Neutron Monitor counts, In Beam Neutron Monitor counts, the amount of time during the run that computer i s av a i l a b l e f o r taking data and the actual amount of time elapsed i n the run. 3) Five TDC's, four of which were started simultaneously on the si g n a l from PI. In d i v i d u a l stops signals originated from P1A, P1B, P2 59 computer tr igger C 212 strobe A D C gate M W P C t r igger c o m p u t e r busy crote_ inhibit dua l gate gen. busy c lear j ~ f rom computer t7 NIM l/TTU 32 ns scaler inhibit FIGURE 3-4 ELECTRONIC LOGIC FOR COMPUTER TRIGGER 60 and the next RF cycle of the accelerator. The remaining TDC was started with G-CV and stopped on the RF s i g n a l . The time of f l i g h t information recorded i n these TDC's was used to determine the incident neutron energy and to r e j e c t X rays. 4) Two ADC's that measured the integrated charge of the pulses from the PIA and PIB photomultipliers. 5) The addresses of the wires that f i r e d i n the multiwire propor-t i o n a l chambers. The on-line program stored the events i n a b u f f e r , 3584 bytes long, that could c o l l e c t about 40 to 50 events before It transferred the buffer to tape as a block. While the program was not processing an event, TDC and chamber data were histogrammed. The on-line histograms could either be printed out or displayed on a graphics terminal. Available for immediate analysis was a f u l l s c a l e r l i s t (see e l e c t r o n i c l o g i c diagrams), the TDC's, ADC's, the multiwire chamber p r o f i l e s and the chamber e f f i c i e n c i e s . E f f i c i e n c y measurements f o r each chamber were displayed i n a histogram i n d i c a t i n g the number of wires f i r e d for each event. Examples of on-line histograms are given i n figures 3—5, 3-6 and 3-7. The data c o l l e c t i o n program copied the on-line histograms and the scalers onto tape at the end of every run. Data c o l l e c t i o n times were of the order of 30 to 60 minutes per run with the detector set to a nominal angle and the target f i l l e d . A se r i e s of runs at each angle were taken a l t e r n a t e l y with target f u l l and empty for approximately 10^ events (approximately a 1% s i g n a l ) . The s i g n a l was estimated by i n t e g r a t i n g the PI to RF time of f l i g h t peak for e l a s t i c a l l y scattered monoenergetic neutrons, An example of the peak i n an on-line histogram i s given i n f i g u r e 3-7. T y p i c a l l y data was c o l l e c t e d at about 3 events per second for target f u l l and 0.5 events per second 61 • © o » 9 » * » a » •*» » — 9- <=> *> » » — » ^  » •*> — 3 O -M _ A* ^ « y* « *> e /i © - B « > » — « 0* /< 3 D "\t •M e o /» .r — • « •*» » yj — &• * J-"V ^ % M *> * 3 ->J • o s • O S • : j i x> — » X — 3 » AJ "Vj — •"I ;y .r o 7 r — _ -c — > •3 » — M • 9Z • => D » 3 s - - i — ^ S *M • a M j 3 X £ C 6 O S O O O O O O O O O O O O O O O O O O O O O O O O O O i T O O O O O O O O O O O t « - 3 0 - 5 C . 0 0 0 0 3 0 0 0 0 0 0 0 0 O 0 3 O 0 0 0 3 D 3 0 S 0 O O 0 0 C 0 0 0 0 3 3 — 3 ><i \ \ > — Q » » £ t h < d / ' i r 3 « « l > l ' M « O O V y«P*.^*<1^ »oI*''*»»\(-" — X — X. o O 3 * « 62 63 64 for target empty. The incident neutron flux per unit neutron monitor count was c a l i -brated at zero degrees, i . e . with the detector i n the beam. The primary proton beam current was reduced from between 300 and 500 nA to between 1 and 3nA so as to keep the rates i n s i n g l e detectors to less than 10^ counts per second. The count rate i n the neutron monitor was reduced consequently to approximately 8 counts per second. At t h i s rate the cosmic ray contribution of about 0.4 S ^ was s i g n i f i c a n t , hence beam o f f runs were made to determine the background counts i n the monitors. Data was taken at neutron beam energies of 319 and 493 MeV. The 319 MeV data was taken at nominal lab angles of 5, 7.5, 15, 22.5, 29.5, 35 and 45 degrees. The 493 MeV data was taken at nominal lab angles of 7.5, 10, 12.5, 22.5, 30 and 45 degrees. 111-2. D i f f e r e n t i a l Cross Sections Measured by Detecting Recoil Protons The r e c o i l protons were detected and momentum analyzed i n a magnetic spectrometer for centre of mass (CM.) angles greater than 65°, because the conjugate scattered neutron was too low i n energy to detect e f f i c i e n t -l y . Between 45 and 65 degrees CM. the t o t a l energy of the r e c o i l pro-tons was measured by a thick s c i n t i l l a t o r as there are no i n e l a s t i c nucleons i n t h i s angular range. The magnetic spectrometer i s shown schematically i n f i g u r e 3-8. In an upstream to downstream order, the f i r s t element of the r e c o i l proton detector was a 250 mm square by 3.2 mm thick s c i n t i l l a t i o n counter denoted SI. Immediately following were three 0.5 m square wire chambers with 4 mm r e s o l u t i o n oriented to measure the XYX co-ordinates. An i d e n t i c a l t r i p l e t 65 MAGNETIC SPECTROMETER s I MWPC 2 ( y ) 6 (J) S2A-D MWPC 8 ( y ) IO (x ) I2 (x) M W P C I ( x ) 3 ( X ) 5 ( y ) M A G N E T MWPC 7 (X) 9 (X) II ( y ) S3 FIGURE 3-8 SCHEMATIC OF APPARATUS TO MEASURE RECOIL PROTONS 66 of XYX chambers was located 0.428 m downstream. The co-ordinates measured by this set of s i x MWPC',s were used to determine the t r a j e c t o r y of incident protons. The redundancy i n the h o r i z o n t a l co-ordinate ensured good e f f i c i e n c y . Four s o l i d angle defining counters, each 37.5 mm wide by 40 mm high by 3.2 mm t h i c k , known as S2 - A, B, C and D, located 2.314 m from the centre of the l i q u i d hydrogen s c a t t e r i n g target were mounted side by side i n front of the momentum analyzing magnet. A s c i n t i l l a t o r , denoted S4, 76 mm high by 191 mm long by 102 mm thick was attached to a s l i d i n g r a i l system that allowed i t to be set behind the S2 counters for t o t a l energy measurements or s l i d c l e a r of the magnet when operating the complete spectrometer. The momentum analyzing magnet was a dipole with a s t e e l return yoke. The f i e l d was surveyed at 2.5 cm i n t e r v a l s to a p r e c i s i o n of 1 part i n 10 . The pole faces were 305 mm deep along the spectrometer axis, 230 mm wide and had a 102 mm a i r gap. The s t e e l yoke had an aperture 535 mm wide by 330 mm deep along the d i r e c t i o n of the spectrometer axis. Table 3-2 gives the magnetic f i e l d values measured while the magnet was powered by 1150 A. The e f f e c t i v e f i e l d length i s given i n table 3-2 as' a function of p o s i t i o n l e f t or r i g h t of the centre of the pole faces. The a i r gap be-tween the pole faces and the aperture i n the yoke were both much larger than the S2 counters, thus eliminating problems with pole face s c a t t e r i n g . The t r a j e c t o r y of a p a r t i c l e leaving the analyzing magnet was mea-sured by two t r i p l e t s of wire chambers each arranged XYX. These chambers were each 1. m square with 4 mm r e s o l u t i o n . The two sets of XYX detectors were separated by 0.553 m. The l a s t element i n the spectrometer was a s c i n t i l l a t o r hodoscope, denoted S3. It was i d e n t i c a l to the array used as the l a s t element i n the neutron detector discussed i n section III—1. TABLE 3-2 Magnet F i e l d Map of Momentum Analyzing Magnet ***** AN X-Y LISTING O f T Hi: MAGNETIC H t l . 0 (GAUSS) ***** X IN. - I S . DO -ft.0(1 -13.00 -12.00 -11.00 -10.00 -9^00 -8,00 -7.0(1 -o.OO -5 .00 -t'.OO -3.0 0 -2,00 -1,00 0,0 1.00 2,00 3,00 '1,0(1 5,00 o.OO 7 . o o 8'.0 0 9'.0 0 to'.00 i f . 00 12'.00 13,00 11.00 IS.00 -4.00 82.0 I 4 0 . o 24o.6 860, I 1643,2 2975,9 '1820,5 7108,7 9340,2 10596,6 11013,0 1 1 124. I 11152,4 11165,6 1117 1,3 1 I 169,5 11161,4 1 I 132,9 11019,7 10590,4 9268.6 7012.3 4705. 1 2850,0 1580, I 831,4 442,0 246,4 142,9 84,2 14.862 Y (INCHE -3.00 89.2 151.1 265.3 485.6 918.8 17S2.5 3130.9 5059.9 7«76.3 9e4I . I 11 159.9 I 1574,3 11675.8 1 1700.5 I 1708.9 11710.4 11709.2 11700.7 11674.1 11572.7 II 156.3 9816.8 7437.7 4986.3 3040.7 1697.4 898. I 481 ,4 269.0 155.9 93.1 15,642 -2.0 0 94,7 Io0.5 284.3 517.6 972.6 1861 .3 3275.6 5228.1 7708.4 10040,6 I 1312.5 I 1707,7 I 1798.1 11819.3 11825.3 I 1825.9 11824.2 I 1816.8 I I 792.1 I 1693,0 1 1269.3 9921 .6 7537,0 5028.5 3085,1 1735.3 914,3 496,2 279.8 161.4 96.8 15,870 -1.00 96.6 164,2 209.7 526.0 990.9 1803.6 3297.6 5260.7 7718.7 10046,3 11336,3 I 1730.5 I 1820,9 1184 1.8 11846.8 I 1847.5 1 1845.3 I 1839.4 11816.2 11720,7 11313.4 1 0001 .7 76J6.6 5113.9 3156.4 1777.3 94 3.8 514.4 289.5 167.8 100.8 15.939 0.0 99,2 167.3 296,3 540,8 1013,0 1925,7 3364,9 5319.8 7790,8 10108,8 I 1354,7 1 177.8,5 I 1825,9 I 1845,3 1 1850,7 11850,5 I 1848,7 J1842,4 11818.6 I 1721.7 11301.1 9951,7 7577,6 5072. I 3117.6 1764,3 935.2 509,0 288,7 167,2 100,6 IS,956 1.00 97.3 165.8 293.6 535,0 1010,3 1918,7 3344,3 5316.4 7782,9 10091 .8 11352.2 11734.0 11821.1 11841,3 I 1846.3 1 1846.5 1 1844,5 11838,0 11813,8 11715.1 11293,I 9950,0 7549,0 5051.5 3110.2 1747,0 926.3 505.4 284,7 165.1 99. I 15.937 2,00 94,9 160,7 285.5 521 ,8 990.2 1889.9 3303.2 5271 .4 7746,5 10059,7 11321.8 1 1705,7 1 1793.7 11814,3 11819,8 1 1820,4 11817,7 11809,8 11784,4 11681 ,8 1 1250,8 9894.6 7481 ,7 4984.8 3058.8 17 09.8 901 .2 490.4 275,4 159,3 96,1 15,862 3.00 89.4 151,4 272,6 496. 1 944,3 1836.1 3199,3 5128,6 7628,5 9898,9 11173.6 11574.2 1 1664.8 11686,8 11692,9 11693.8 11688,9 1 1677,4 11649,6 11542.2 11088.4 9743.3 7354.3 4840,8 2978.9 1658.5 857,7 468.8 262.7 150,0 90,6 , 15,626 4,00 83,0 140,5 249,4 459,5 887,7 1712,3 3027.8 4894.4 7207,7 9380.5 10620,7 11011,3 11112,1 11 141,9 11144,0 11144.4 11139,6 11 120,2 11086.7 10966,4 10513,1 9207,3 6936,1 4615.2 2815,8 1548,0 806.3 434,8 241 ,4 139,4 83.6 14.839 THE ENTRIES IN THE LAST LINE ARE THE EFFECTIVE FIELD LENGTHS IN INCHES. THE EFFECTIVE FIFLD LENGTH AT Y = (1NTEGRAL(B(X,Y)*DX))/BAV , WHERE BAV = 11846.3 GAUSS = THE AVERAGE MAXIMUM F I E L D . 68 The monitors used i n the " r e c o i l proton" phase of the experiment were the same as those used i n the "neutron" h a l f of the measurement and are described i n section I I I - l and i n Chapter I I . Since the monitors were i d e n t i c a l , a d i r e c t normalization of the r e c o i l proton d i f f e r e n t i a l cross section was made. The absolute number of incident neutrons was determined from the monitors c a l i b r a t e d i n an experiment outlined i n the introduction and f u l l y described i n reference D2. The neutron detector e f f i c i e n c y was c a l i b r a t e d by an associated p a r t i c l e experiment. R e c o i l protons were detected i n a telescope and e l a s t i c events where selected by time of f l i g h t and dE/dx. For each of these protons a scattered neutron should have been observed by the neutron detector. Since the e f f i c i e n c y for proton detection was 100%, the r a t i o of neutron-proton coincidences to proton singles gave the e f f i c i e n c y of the neutron detector. The monitors were then c a l i b r a t e d by placing the neutron detector at zero degrees. The constant of p r o p o r t i o n a l i t y r e l a t i n g the neutron monitor rate to the t o t a l neutron f l u x i s approximately 900 neutrons per monitor count. The signature of a detected proton was the e l e c t r o n i c coincidence S1-S2-S3 where S2 was any of the counters S2 A, B, C or D and S3 was any of the counters S3 A, B, C,... , G or H. The e l e c t r o n i c l o g i c f o r the r e c o i l proton experiment i s shown i n f i g u r e 3-9. The S1-S2-S3 coincidence was the computer t r i g g e r f o r the magnetic spectrometer phase of the experiment and i t started a very s i m i l a r procedure for taking an event as was described i n section I I I - l . The computer interrupt c i r c u i t , the busy s i g n a l and the busy clear generator were the same as before. The data recorded by the on-line program was the following: 1) The b i t pattern i n d i c a t i n g which of the S2 and S3 counters f i r e d . 69 S I A S 2 S 4 S3 A B C D A B C D E F G H I A D C _ TDC I stort \ 71\ 7K 7T\ 7]\ S 2 T D C | : 2 _ stop T D C II stop S .S , T D C | :3_ stop S3 S j SgS^ "tolaI energy" tr igger SjSgSS spectrometer \ J t r igger FIGURE 3-9 ELECTRONIC LOGIC FOR RECOIL PROTON EXPERIMENT 70 Since each S2 counter e f f e c t i v e l y defined a measurement at a p a r t i c u l a r s c a t t e r i n g angle, the b i t pattern was used i n the off-line analysis to separate out four d i f f e r e n t data sets. 2) The number of counts with the e l e c t r o n i c signatures S1*S2*S3, [CL + CR]-CV,G-CV, Z1-Z2-Z3, the l i v e time and the r e a l time as read from the s c a l e r s . 3) Three times of f l i g h t with SI as a s t a r t ; the stops were any S2, any one or more S3 and the next RF cycle of the accelerator. The TOF for G'CV to the RF was also read. 4) Three ADC's that integrated the signals from SI, the sum of S2 A, B, C and D and the sum of S3 A, B, C, G and E. 5) The addresses of the wires that f i r e d i n the s i x 0.5 m square chambers i n the upstream ha l f of the spectrometer. The addresses of the six 1.0 m square chambers were then read. As before the events were stored i n a buffer by the on-line computer and then written to tape as blocks. The program displayed the s c a l e r s , histograms of the times of f l i g h t and ADC spectra, the wire chamber pro-f i l e s and the chamber e f f i c i e n c i e s . A l l of the scalers and on-line histograms were written to tape a f t e r each run. The spectrometer data was c o l l e c t e d by moving the detector to the required nominal angle. This was accomplished by al i g n i n g cross hairs on the back of the apparatus with f i d u c i a l marks inscribed on the f l o o r . T y p i c a l l y , two p a i r s of target f u l l and empty runs were taken at each, angle and energy. S u f f i c i e n t events were taken to give approximately a 1% error on the s i g n a l f o r each S'2 counter. In p r a c t i c e , t h i s amounted to about 80,000 events with the target f u l l and 2000 events with.the target empty. An average event rate was 13 per second f or target f u l l and about 1.5 per second for target empty. 71 At each angle the momentum-analyzing magnet current was set to bend r e c o i l protons from np e l a s t i c s c a t t e r i n g through 120 mrads. This e l i m i -nated v a r i a t i o n s i n the acceptance and r e s o l u t i o n of the spectrometer. The spectrometer data at 319 MeV was taken at nominal lab angles from 5° to 55° i n 5° steps. At 493 MeV the nominal lab angles were 5° to 60° i n 5° steps. The t o t a l energy data was measured using the t h i c k s c i n t i l l a t o r , S4, f o r nominal lab s c a t t e r i n g angles of 55° for 319 MeV incident neutrons and 60° for 493 MeV neutrons. Therefore the widest angle data was measured i n two ways to ensure that the low energy r e c o i l protons were not l o s t from the spectrometer by range or multiple scat-t e r i n g . The t o t a l energy spectrometer i s shown i n fig u r e 3-10. The t o t a l energy measurement used the same el e c t r o n i c s and online computer code as the magnetic spectrometer measurement. Two computer tr i g g e r s were used, S1-S2 and S1-S2-S4. When the l a t t e r t r i g g e r was i n use the 100 mV di s c r i m i n a t i o n l e v e l on the e l e c t r o n i c s f or the S4 counter rejected some very low energy p a r t i c l e s . Each event had the b i t pattern f o r the latches, the TOF's from the TDC's and the addresses of the wires that f i r e d i n the f i r s t s i x chambers. The information that was d i f f e r e n t from the spectrometer data i s : 1) The time of f l i g h t started by SI and stopped by S3 was replaced by SI to S4. 2) The ADC i n t e g r a t i n g the s i g n a l from S3 was changed to S4. 3) The sca l e r s were changed to the following s i g n a l s , S1-S2 or SI-S2-S4 depending on the trigger,[CL + CR]•CV, G-CV, Z1-Z2-Z3, the l i v e time and the r e a l time. The data was processed by the on-line program exactly as for the spectrometer data and the data was taken using the same procedure. The voltage on the photomultiplier viewing S4 was found experimentally 72 TOTAL ENERGY SPECTROMETER z S I MWPC 2 ( y ) S 2 A D THICK SCINTILLATOR 4 ' I ! 6 (*) M W P C I ( x ) 3 (X) 5 ( y ) S4 FIGURE 3-10 SCHEMATIC OF APPARATUS TO MEASURE RECOIL PROTONS 73 by r a i s i n g i t u n t i l the observed peak was no longer cut :off at the low energy end. This voltage was 1850 V corresponding to an average pulse height of 1.5 v o l t s . The S4 s i g n a l was attenuated by a fa c t o r of 10 to keep the high energy end of the spectrum within the range of the ADC. The voltage and attenuation agree w e l l with an estimate made of the l i g h t G2 G3 output of the s c i n t i l l a t o r ' and the photomultiplier tube gain. The data rates were comparable with the rates f o r the spectrometer data. Roughly 40,000 events were taken with the target f u l l and 2000 with the target empty for each energy. No data analysis was performed on-line for any phase of t h i s experiment. A l l the data was transferred by tape to the computing centre at UBC for off-line a n a l y sis. 74 IV. Analysis of D i f f e r e n t i a l Cross Section Data The data analysis was performed off-line on the UBC Amdahl 470 V/6. The procedure to reduce the neutron data, the spectrometer data and the t o t a l energy counter data i s described here. Conceptually, the same approach was used to analyze a l l of the measurements. A multipass system was employed that systematically calculated the d i f f e r e n t i a l cross section from the i n i t i a l data. The d e t a i l s of how each pass of the analysis program was applied to the three measurements i s discussed here. IV-1. Analysis of Neutron Data The on-line histograms and the scalers were printed and examined as the f i r s t stage of the analysis. Runs with c l e a r l y i d e n t i f i e d e l e c t r o n i c f a u l t s were rejected. The next pass consisted of a computer code that read the data tapes one run at a time. A crude s e l e c t i o n of e l a s t i c a l l y scattered events using loose cuts on the PI to RF TOF was made and the tracks i n the wire chambers were f i t t e d f o r those events. The systematic errors introduced by the cuts are described i n chapter V. The f i r s t cut required that at le a s t two h o r i z o n t a l and two v e r t i c a l chambers f i r e d . A few percent of the events f a i l e d t h i s t e s t . These events were uniformly d i s t r i b u t e d i n the PI to RF time of f l i g h t and had a t r a n s i t time from PI to P2 equal to that observed for the ¥ rays produced by np—»dTT °. The events were therefore assumed to be low energy background Y -rays, possibly from neutron absorption. A cut was made on the t r a n s i t time from PI to P2 such that events, where P2 f i r e d before PI, were eliminated. A sample spectrum i s given i n figur e 4-1 and the cut p o s i t i o n i s shown. These events were assumed to be due to v e r t i c a l cosmic ray showers as confirmed by the observations that they were d i s t r i b u t e d uniformly over the PI to RF TOF and were poorly C O U N T S 3 0 0 0 -neutrons I oo 2 0 0 0 ^rays o CUT 1 0 0 0 2 0 "backward" going particles i O o 0 o 0 0 o 0 o ° ° o o o 3 0 a 1 4 0 5 0 6 0 7 0 P,-P2 (chan) FIGURE 4-1 PI TO RF TIME OF FLIGHT 76 f i t t e d by the track f i t t i n g routines. This cut removed on the order of 2% of the raw t r i g g e r s and introduced approximately a 1% v a r i a t i o n i n the f i n a l s i g n a l . Two cuts were made on the PI to RF TOF. A t y p i c a l spectrum with the cuts indicated i s shown i n f i g u r e 4-2. The neutrons i n the remaining peak were from the q u a s i - e l a s t i c part of the d(p,n)2p reaction. These cuts were wider than the f i n a l RF cuts and had no e f f e c t on the d i f f e r e n -t i a l cross section. They served merely to reduce the number of i n e l a s t i c events that were analyzed. Straight l i n e tracks were f i t t e d to the wire chamber data that survived the cuts-approximately 50% of the raw data. The wire co-ordinates were randomized to smooth histograms of parameters calculated from the wire chamber data. The corrected co-ordinate was selected randomly from a square d i s t r i b u t i o n +2 mm wide and centred on the exact wire p o s i t i o n . The procedure for assigning a track to an event depended on the number of chambers that f i r e d . If two chambers had h i t s the l i n e was calculated a n a l y t i c a l l y from the corrected wire co-ordinates. This was possible only i f both chambers contained s i n g l e h i t s or adjacents of three or les s wires. A l l multiple h i t data was rejected. An adjacent was defined as two or more wires f i r i n g that are immediately beside each other. For two and three wires the average p o s i t i o n was used as the co-ordinate but for four or more wires each was taken i n d i v i d u a l l y and hence the event was rejected. Three or four chamber tracks were found by doing a le a s t squares l i n e a r f i t (z=m x+a ; z=m y+a ) to every combination of singles and x x y y adjacents. The procedure was to loop over a l l of the h i t s i n each chamber storing the calculated slope(m), intercept(a) and square of the error on 240 200 o Target full x Target empty 160 120 h-2 8 801 40 CUT O O CUT 6 ,X x X' * x xo x x xo ° 9 x § x x o x x8 x x • i i i i i i i i 1 60 70 80 90 100 110 120 130 140 150 P (-rf (chan) FIGURE 4-2 PI TO RF TIME OF FLIGHT 78 the intercept ( cr* ) f o r each f i t . The f i t with the lowest value of cr^ was chosen. The square of the error on the intercept was calculated by ( r ^ - l ^ S x i 1 ) / ( K S ^ - ( S x i ) * ) 4 - 1 i L I where x. i s the co-ordinate of a h i t i n the i — wire chamber, N i s the 1 number of chambers and i s given by Z l = S l j L - a x ~ m x x - ) 4 - 2 th where i s the p o s i t i o n of the i — w i r e chamber, a^ i s the intercept of the f i t and m^ i s the slope. The o r i g i n of the co-ordinate system f or the detector was located at the centre of the carbon convertor and the p o s i t i v e z axis was perpendicular to the face of the carbon and pointed i n the downstream d i r e c t i o n . The x-axis was h o r i z o n t a l and the y-axis was v e r t i c a l . Equations 4-1 and 4-2 apply equally w e l l to the x and y chamber co-ordinates. x A minimum q u a l i t y f i t , \ 300, was demanded. This l i m i t was approximately the worse error expected from the chamber geometry that was used. The value was measured by p l o t t i n g the number of tracks f i t x versus and s e t t i n g the cut i n the plateau region. If there was no track with O"^ N 300 then the event was eliminated for three chamber f i t s . Four chamber f i t s were reanalyzed by f i t t i n g a l l of the possible three chamber combinations. The best f i t was taken or the event was cut i f i t s t i l l f a i l e d the t e s t . Once the tracks were :f I t , the chamber e f f i c i e n c i e s were calculated. The point where the track intercepted the unfired chamber was calculated and histogrammed. The PI to RF TOF was also histogrammed for each of these events. T y p i c a l l y the chamber e f f i c i e n c i e s were 98% with an o v e r a l l 79 f i t t i n g e f f i c i e n c y of about 96% f o r the whole system. The computer code wrote on tape and paper the data required by the next pass. The s c a l e r s , PI to RF TOF, and the e f f i c i e n c y histograms for each of the wire chambers were printed out. For each raw event, a p a r t i a l l y analyzed version was written to tape. The new tape, c a l l e d a skim tape, contained the event structure l i s t e d below: 1) The PI to RF, PI to P2, PI to P1A and PI to P1B times of f l i g h t . 2) The h o r i z o n t a l chamber f i t i f o~A was less than 300. This included the slope (m x), intercept (a ) and the square of the error on the intercept ( CT^ ). x 3) The v e r t i c a l chamber f i t i f CT^ _ < 300. The parameters were the slope (m^), intercept ( ay) a n ^ t n e square of the er r o r on the intercept c o £ )• 4) The randomized co-ordinates of a l l the h i t s i n the veto wire chamber. The next pass read the skim tape and events were eliminated by cuts based on the chamber data. The s e n s i t i v i t y of the r e s u l t s to these cuts w i l l be discussed i n chapter V. A track was required i n both the v e r t i c a l and h o r i z o n t a l planes. This cut removed about 4% of the events. The o f f l i n e veto was applied to the data. The v e r t i c a l track was extrapolated back to the veto chamber and compared with the p o s i t i o n of each of the wires that f i r e d . The event was rejected i f the chamber data agreed with the extrapolation to +50 mm for the 319 MeV data. The analysis at 493 MeV used a +5 mm tolerance because the chamber was noisy at t h i s energy and produced accidental vetoes. An a l t e r n a t i v e method for I d e n t i f y i n g protons was to study the s c a t t e r i n g angle of the p a r t i c l e COUNTS 300 200 100 _L 200 -100 0 FIGURE 4-3 HORIZONTAL CARBON PROFLE 100 200 mm oo o COUNTS 300 PUJI Lr u-TnJl] f i n 200 100 •200 FIGURE 4-4 -100 0 VERTICAL CARBON PROFILE 100 200 mm oo 82 i n the carbon. Since the majority of protons only multiple scatter i n the carbon, t h e i r s c a t t e r i n g angles are less than a few degrees. It was found that a +5 mm acceptance on the veto chamber v i r t u a l l y eliminated accidental vetoes but did not change the scattering angle d i s t r i b u t i o n . T y p i c a l l y , the number of events vetoed o f f - l i n e was less than 1% f o r both energies. The edges of the carbon convertor had a d i f f e r e n t e f f i c i e n c y from the centre as incident neutrons and the charged reaction products were transmitted through various thicknesses of material. The e f f e c t was eliminated by defining a f i d u c i a l region i n the centre of the carbon, 400 mm square. The cut was made on the ho r i z o n t a l and v e r t i c a l intercepts of the MWPC tracks. A t y p i c a l h o r i z o n t a l and v e r t i c a l d i s t r i b u t i o n .of events across the carbon i s shown i n figures 4-3 and 4-4. The number of events eliminated by the v e r t i c a l and h o r i z o n t a l carbon cuts together was approximately 40%. Figure 4-5 i s a histogram of the number of events versus scattering angle i n the carbon Qc . The angle i s defined as the polar angle between a track o r i g i n a t i n g at the centre of the l i q u i d hydrogen target and the track defined by the MWPC's with.the Intersection point h a l f way through the carbon. The ordinate Is proportional to do^ / d i l SINO^ , where 0\ Is the cross section f o r the reaction C(n,x) such that x i s a charged p a r t i c l e . The d i s t r i b u t i o n i s si n u s o i d a l to within a few percent at angles less than 5 degrees. Beyond 17 degrees t h i s approximation f a i l e d completely. Figure 4-6 i s a s i m p l i f i e d perspective of the neutron detector i l l u s t r a t i n g the change i n e f f i c i e n c y as a function of 0 e and the X and Y intercepts of the track. Small s c a t t e r i n g angles are inde-pendent of 4> , the azimuthal angle about the incident track. In other words a cone made by r o t a t i n g the scattered track about the incident COUNTS FIGURE 4-5 POLAR SCATTERING ANGLE IN CARBON SIMPLIFIED PERSPECTIVE OF NEUTRON DETECTOR ILLUSTRATING VARIATION OF ACCEPTANCE OVER CARBON GEOMETRICAL ACCEPTANCE IS REDUCED IN THE CASE SHOWN ABOVE FIGURE 4-6 85 track, i s intersected completely by P2. However, for sc a t t e r i n g angles greater than 18° t h i s i s no longer true for tracks o r i g i n a t i n g near the edge of the f i d u c i a l region of the carbon. Consequently the e f f i c i e n c y of the detector varies as a function of distance from the centre of the carbon. A cut of 17° was made on 8e , eliminating approximately 50% of the data. The d i f f e r e n t i a l cross section did not strongly depend on the cut (that i s for angles less than 17°); the v a r i a t i o n was 0.2% at 493 MeV and 0.1% at 319 MeV. Figure 4-7 i s a flow chart i n d i c a t i n g the cuts that were made at each step of the analysis and the histograms that were printed. The second pass computer code printed the sc a l e r s , the PI to P2 TOF and the PI to RF TOF histograms before any cuts were made, a histogram of the veto chamber.co-ordinates of events that were vetoed o f f - l i n e , t h e v e r t i c a l and h o r i z o n t a l carbon p r o f i l e s , a histogram of 9 C and the PI to RF TOF af t e r a l l cuts. The f i n a l PI to RF TOF along with the scalers was also written to a disk f i l e that was the input f o r the t h i r d pass program. This program, known as "Neutron - Analyze", calculated the d i f f e r e n t i a l cross sections. The f i n a l pass computer code read i n a l l of the data for a p a r t i c u l a r angle and energy, the PI to RF TOF histograms and scalers for a l l of the target f u l l runs and then for a l l of the target empty runs. The h i s t o -grams and scalers were also read i n f o r the "zero degree" or i n beam runs that provided the normalization for the d i f f e r e n t i a l cross section. The d i f f e r e n t i a l cross section f o r e l a s t i c neutron-proton s c a t t e r i n g was calculated as dig* A i l cn. 4 - 3 FIRST PASS PROGRAM TWO WIRE CHAMBERS FIRED IN "X" AND "Y" PLANES PI TO P2 TOF CUT SECOND PASS PROGRAM TRACK IS FIT IN BOTH "X" AND "Y" PLANES OFFLINE VETO IS APPLIED 200 mm CARBON CUT APPLIED ON "X" AND "Y" PROFILES 17° CUT ON SCATTERING ANGLE IN CARBON PI TO RF TOF CUT FIGURE 4-7 FLOW CHART OF NEUTRON ANALYSIS 87 where R g (8 ) i s the si g n a l rate at a s c a t t e r i n g angle of 9 , i s the rate with the detector i n the beam, ri i s the number of target protons per unit area and A -O. i s the s o l i d angle subtended by the neutron detector. The e f f i c i e n c y of the neutron detector as a function of energy i s denoted »^  (T). The e f f i c i e n c y of the detector at 0°, where the energy i s that of the incident beam (319 or 493 MeV), i s known as r^ , . The s t a t i s t i c a l error on the d i f f e r e n t i a l cross section i s given by £<T(G) = — J * — £ R s l e> 4 " 4 The s i g n a l rate i s the normalized f u l l minus empty rates given by R s ( 0 ) = NF(e> _ N M T(Q) 4 - 5 F(MT) where N i s the number of neutrons detected with the target f u l l F(MT) (empty) and s i m i l i a r l y M i s the number of monitor counts f o r target f u l l (empty) runs. The error derived from Poisson s t a t i s t i c s i s £D I =R s i9) r r + _L_ + _ ! _ + J _ 4 - 6 The rate at 0° i s 4 - 7 where N ( 9 = 0) i s the number of neutrons detected at Q'.and M q i s the number of monitor counts. The number of target protons per unit area i s calculated by n t = N0p.W.t 4 - 8 / A where N q i s Avogadro's number, ^ i s the density, t i s the length of the target, W i s the number of atoms per molecule and A i s the molecular weight. 88 The number of detected neutrons was calculated by integrating the PI to RF time of f l i g h t histograms +4 ns (+20 channels) from the peak. The peak was determined for target f u l l runs by f i t t i n g the TOF spectra with a Gaussian plus a cubic polynomial background. Target empty data with a su i t a b l e peak were f i t t e d i n the same manner. However, i f the d i s t r i b u t i o n was f l a t , the peak channel was supplied by v i s u a l l y examining the histograms. T y p i c a l l y the peak p o s i t i o n of the previous f u l l run was used. The peak positions f o r the zero degree runs were a l l determined by hand. The r e s u l t s of the: i n t e g r a t i o n were i n s e n s i t i v e to the upper cut l i m i t and, for small changes i n the lower cut l i m i t , varied by a maximum of 1.3% and 493 MeV and 0.5% at 319 MeV. The monitor used to determine a l l of the rates was the Wide Angle Neutron Monitor. I t was corrected f or accidental vetoes, a 0.1% e f f e c t . The monitor was compared with the In Beam Neutron Monitor and the Primary Proton Beam Monitor and i t had a 3.8% s t a b i l i t y at 493 MeV and a 1.5% s t a b i l i t y at 319 MeV. The s i g n a l was calculated as the difference between the average f u l l and empty rates. If the % X per run was greater than one by an improbable amount (approximately le s s than 10% chance) the data was s p l i t up into subsections of consecutive runs that were s i m i l a r . This happened because of s h i f t s i n the cyclotron and beam tune. Table 4-1 i s a l i s t of the s i g n a l , the s t a t i s t i c a l error on the s i g n a l and the "X. f o r each angle at 319 MeV and 493 MeV. The same zero degree runs were used to normalize every angle at a p a r t i c u l a r energy. The number of neutrons detected i n target f u l l runs was corrected f or the t o t a l cross section. The formula for the correction i s 89 TABLE 4-1 2 Signal and OC f o r Neutron Data at 319 and 493 MeV 319 MeV Lab. Angle Signal /n for Target % /n for Target Degrees x!0~3 F u l l Empty 5.0 1.382 + .0827 0.185 0.258 7.5 1.380 + .0300 0.738 0.304 7.5 1.338 + .0859 0.0 0.0 15.0 1.067 + .0172 0.25 0.15 15.0 1.092 + .0296 0.0 0.0 22.5 0.7160 + .0139 1.349 1.366 22.5 0.7238 + .0081 0.502 0.514 22.5 0.7538 + .0292 0.0 0.0 29.5 0.4354 + .0136 1.15 0.0 29.5 0.4449 + .0075 1.098 0.153 35.0 0.2953 + .0047 1.212 0.456 35.0 0.2838 + .0131 0.0 0.0 45.0 0.1122 + .0073 0.006 0.0 493 MeV 7.5 2.789 + .0700 0.995 2.403 10.0 2.472 + .0458 0.0 0.123 12.5 2.232 + .0379 0.0 0.0 22.5 1.187 + .0145 0.014 3.128 30.0 0.680 + .0102 0.089 0.005 45.0 0.198 + .0136 0.0 0.0 45.0 0.181 + .0092 0.416 1.023 90 4-9 where N m i s the measured number of neutrons, n i s the number of pro-o t tons per unit area i n the f u l l l i q u i d hydrogen target and O^p i s the t o t a l neutron proton cross section. The monitors for zero degree runs were corrected f o r the beam o f f rate by M° = M " 1 + M t ° ^ 4 - 1 0 where M i s the number of events i n the Wide Angle Monitor f o r a beam off run, t„ i s the l i v e time of the beam off run, M™ i s the number of B o monitor counts f o r a zero degree run and t i s the l i v e time of a zero m degree run. Equation 4-7 f o r the zero degree rate becomes R = N C ° ' -4 4 - 1 1 M C o G4 The s o l i d angle was calculated by assuming a point source and a detector that was a rectangular plane, A-ft = a r c W i l x » - X , m a - S p ) 1 1 } ptlx a-xO x«-l**-*p) 4 + f P 1 J -^arc-Va^S U>- X » U S> ) 1 4 - 1 2 91 where the point at the centre of the l i q u i d hydrogen target i s r ^ = '(x, y , z ) and the rectangle i s bounded by x = x., x = x„, y = y and y = y„. p p 1 z 1 z The rectangle was the f i d u c i a l area of the carbon; x = +200 mm, y = +200 mm.and the point r was (0,0*5480) mm. The calculated s o l i d angle was -3 4.986 x 10 steradians. Averaging over the volume of the l i q u i d hydrogen target was less than a 0.1% e f f e c t . The experiment to measure the energy dependence of the neutron counter e f f i c i e n c y was described b r i e f l y i n chapter I I I . The d e t a i l s of the experiment and the data analysis are well described i n R. Dubois' D2 thesis . Figure 4-8 shows a f i t to the data i n inverse k i n e t i c energy. The parameters of the f i t are (. T T 4 T a where T i s the. k i n e t i c energy i n MeV. The error matrix i s given i n table 4-2. Table 4-2 Error Matrix f o r Cubic F i t to E f f i c i e n c y O-^ .16701 x 10~ 5 -.13521 x 1 0 _ 2 .33287 -24.546 CTV -.13521 x 10" 2 1.1120 -277.36 . 20629 * 7 <T^ .33287 -277.36 70030.0 -.52513 x 10 (X. -24.546 20629 -.52513 x 10 7 .39600 x 10 9 The degree of the polynomial f i t was determined by s t a r t i n g with a l i n e a r f i t and then increasing the degree u n t i l the errors on the parameters were larger than the parameters. This occurred f o r a qu a r t i c . A v a r i e t y of kinematic quantities such as momentum, t o t a l energy, v e l o c i t y and k i n e t i c energy were t r i e d and the f i t with the best IC - 0.253 per data point f o r inverse k i n e t i c energy - was chosen. The e f f i c i e n c y was cal c u l a t e d from equation 4-13 f o r the incident 92 1 2 3 4 5 6 7 8 T'l(IG73MeV~l) FIGURE 4-8 EFFICIENCY AS A FUNCTION OF INVERSE KINETIC ENERGY 9 3 and scattered neutron energies and substituted into equation 4 - 3 to ca l c u l a t e the d i f f e r e n t i a l cross section. These values are corrected i n chapter V for systematic e f f e c t s and the f i n a l r e s u l t s are also tabulated. IV - 2 . Analysis of the Spectrometer Data The d i f f e r e n t i a l cross section, measured by detecting protons, cannot be normalized i n the same way as the neutron data, by moving the detector to zero degrees. The absolute normalization depends on the c a l i b r a t i o n of the monitors. The formula for the d i f f e r e n t i a l cross section i s = _ J ( N l _ NT "IK d i l l n t A i l l M * M M T ) dLJlc.fv 4 - 1 4 where n^ _ i s the number of protons per unit area i n the target, A - f l . i s F(MT) the s o l i d angle of the proton detector, i s the number of protons F(MT) detected with the target f u l l (empty), M i s the number of incident neutrons monitored with the target f u l l (empty), K i s the number of incident neutrons per monitor count and djfllab/d-Q. cm i s the Jacobian from the lab to the centre of mass frame. The s t a t i s t i c a l error i s given by e<r<e)--K / i + J L T + _ L + _L n tAjaV N; IC H H The value of K i s given i n terms of experimental observables by K = N 0 / M O ^ C T . ) 1 6 where N /M i s the number of neutrons measured per incident monitor o o count for the zero degree neutron data and rj^  ( T q ) i s the e f f i c i e n c y calculated from equation 4 - 1 3 at the incident beam energy, T^. The monitors for the proton phase of the experiment remained i d e n t i c a l to those of the neutron phase so that the c a l i b r a t i o n was not altered. The proton data was analyzed as s i m i l a r l y as possible.to the neutron 94 data to eliminate systematic d i f f e r e n c e s . The on-line histograms and the scalers were printed out. Runs with obvious e l e c t r o n i c f a u l t s were deleted. The f i r s t pass computer code f i t t e d tracks to the wire chamber data but made no cuts. The track f i t t i n g was done with exactly the same computer codes as for the neutron data. The front 0.5 m chambers were f i t separately from the rear 1.0 m chambers. This gave an incident p a r t i c l e track and a track for the e x i t p a r t i c l e a f t e r i t had completed i t s t r a j e c t o r y through the momentum analyzing magnet. The chamber e f f i c i e n c i e s were calculated and missed wires were histogrammed. The o v e r a l l track f i t t i n g e f f i c i e n c y i n the ho r i z o n t a l plane (the v e r t i c a l plane was not used i n the analysis) was t y p i c a l l y 99.9%. The improvement i n the e f f i c i e n c y i s consistent with the improvement of the charged p a r t i c l e t r i g g e r compared to the neutron t r i g g e r . The co-ordinate system used had i t s o r i g i n at the centre of the momentum analyzing magnet, the p o s i t i v e z" axis was pointed downstream, the x axis was h o r i z o n t a l and the "y axis was v e r t i c a l . The printed output of the f i r s t pass program included a l l of the sc a l e r s , the histograms of chamber wires that f a i l e d to f i r e , the ho r i z o n t a l p r o j e c t i o n of the l i q u i d hydrogen target reconstructed from the incident p a r t i c l e tracks, a histogram of the scattered p a r t i c l e momenta that were calculated approximately from the bend angle, the SI to S3 TOF spectrum, the SI to RF TOF, a separate histogram of the bend angle for each S2 counter and an SI to RF TOF spectrum for events used to compute the e f f i c i e n c y histograms. Scatter plots of the SI to S3 TOF versus momentum and of the SI to RF TOF versus momentum were made. The print-outs were examined v i s u a l l y f o r bad runs due to e l e c t r o n i c f a u l t s or equipment f a i l u r e . 95 The f i r s t pass program output a p a r t i a l l y analyzed event to tape for each raw event read i n . The new tape was c a l l e d a "proton skim tape" and i t contained a scaler summary for the run as w e l l as the following event by event data: 1) The b i t pattern i n d i c a t i n g the s c i n t i l l a t o r s that f i r e d . 2) The sca l e r s f o r (CL + CR)•CV, G-CV, the number of events to date, the l i v e time and the r e a l time. 3) The times of f l i g h t started by SI and ended on S2, S3 and the next RF cycle from the accelerator. 4) The ADC pulse height for SI, S2 A, B, C or D and S3 A, B,..., G or H. F F F F t a . 5) The slope m (m ), intercept a (a ) and the value of OT w x y x y F (0~ ) ' for the h o r i z o n t a l ( v e r t i c a l ) f i t to the track i n the front s i x ay 0.5 m square wire chambers. B B B B A 6) The slope m (m ) , intercept a (a ) and the value of ( O* ) r x. - y ' r x y M o.y for the h o r i z o n t a l ( v e r t i c a l ) f i t to the track i n the rear s i x l.m square wire chambers. The proton skim tape data was read into the second pass computer code. This program made a l l of the cuts and calculated the d i f f e r e n t i a l cross section and the s c a t t e r i n g angle. I t was run twice, the f i r s t time with no cuts f o r a f u l l and an empty run at each angle and both energies. The cuts were determined from t h i s output, included i n the program and the code was rerun with a l l of the f u l l and empty runs. Figure 4-9. i s a flow chart of the cuts that were put on the spectrometer data. The histograms and s c a t t e r plots that were printed are also shown. The f i r s t t ests were on the b i t pattern. Only events with one S2 counter having f i r e d were accepted. The p r o b a b i l i t y of getting two events In one beam burst was n e g l i g i b l e so these events were eliminated. The SINGLE S2 COUNTER FIRED CONSISTENT S3 COUNTERS FIRED TRACK HIT S2 ARRAY WITHIN ± 20 mm FRONT AND BACK TRACKS INTERSECTED WITHIN ± 50 mm TRACK EXTRAPOLATES BACK TO LH 2 TARGET BEND ANGLE IN MAGNET WAS AT LEAST 0.03 rad. DEUTERONS WERE CUT FROM SI TO S3 TOF VS. MOMENTUM SCATTER PLOT HIGH MOMENTUM BACKGROUND WAS REMOVED INELASTIC PROTONS WERE CUT FROM S2 TO RF TOF VS. MOMENTUM SCATTER PLOT FIGURE 4-9 FLOW CHART OF RECOIL PROTON ANALYSIS 97 b i t pattern for the S3 hodoscope was checked to see i f the counters that f i r e d overlapped each other, i f not, the event was eliminated. The events that f a i l e d the b i t pattern t e s t s were less than 0.5% of the data and were l i k e l y due to cosmic ray showers. A histogram of the b i t pattern was output f o r each run and studied for changes i n counter e f f i c i e n c y or any other anomaly. The next test demanded that the f i t t e d l i n e to the incident track pass through a h o r i z o n t a l road centred on the middle of the S2 counter array and +95 mm wide (that i s +20.mm wider than the S2 array). T y p i c a l l y , l e s s than 0.3% of the events were eliminated by t h i s cut. The intercepts of the incident and e x i t tracks, which are the tracks extrapolated to the centre of the magnet, were compared and the events were accepted i f they agreed to within +50 mm. The average loss of events from t h i s cut was less than 0.4%. These events were due to pro-tons that underwent nuclear s c a t t e r i n g i n the spectrometer or pions that decayed i n f l i g h t . Figure 4-10 i s a histogram of the difference between the incident and e x i t track i n t e r c e p t s . The incident tracks were extrapolated back to the target p o s i t i o n (z = -2313 mm) and a histogram was made of the proje c t i o n of the target on the h o r i z o n t a l axis. Cuts were made to remove events that were from outside of the l i q u i d hydrogen volume. The cut positi o n s were determined by making a subtraction of the target empty pr o j e c t i o n from the target f u l l . Where the histogram subtracted to zero determined the upper and lower cut l i m i t s . Roughly 2% of events- from target f u l l runs were cut while t y p i c a l l y 15% of events from target empty runs were removed. The res o l u t i o n of the reconstruction of the target p r o f i l e did not allow the windows nearest the l i q u i d hydrogen or the aluminum dome to be separated completely. A target p r o f i l e subtraction Is: given i n fi g u r e 4—11. 98 COUNTS 20000 15000 10000 5000 0 133 -67 0 67 133 FIGURE 4-10 mm DIFFERENCE BETWEEN INCIDENT AND EXIT TRACK INTERCEPTS 800 • TARGET FULL o TARGET EMPTY 700 600 500 CO r-Z o (J 400 300r 200 00 o • mo. oo e P' « » ° i-* % » o o M o o ° ? » < > « % o 0 o 0 o o 0 o < > * » " * % o » » -300 -200 -100 100 X (mm) FIGURE 4-11 LIQUID HYDROGEN TARGET PROFILE 100 The bend angle was calculated as 6B = a r c T ^ n . ( m * ) — arcTflun. ( m* ) 4 - 1 7 where m i s the slope of the f i t to the ho r i z o n t a l p r o j e c t i o n of the e x i t track and s i m i l a r l y m i s the same f o r the track entering the spectrometer. A cut was made to re j e c t s t r a i g h t tracks, © B 4 0.03 radians. These events were t y p i c a l l y 0.01% of the data and were a t t r i -buted to gamma rays. Data that survived the cut were histogrammed f o r bend angle according to which S2 counter f i r e d . A t y p i c a l histogram i s shown i n f i g u r e 4-12. The f u l l width at h a l f maximum y i e l d s a r e s o l u t i o n of A Pa = &P_ = 12%. The momentum was calculated from the bend angle by P = 3.0 * \0'X \ ft ' d l 4 - 1 8 9 8 J where p i s the momentum i n MeV/c, i s the bend angle i n radians and X B ' d l i s the l i n e i n t e g r a l of the magnetic f i e l d along the p a r t i c l e t r a j e c t o r y i n units of Tm. The e f f e c t i v e f i e l d length, defined as ft » Al 4 - 19 BAV where BAV, the average maximum f i e l d , Is tabulated i n table 3-1 for a current of 1150 A. The e f f e c t i v e f i e l d length as a function of the ho r i z o n t a l distance from the centre of the magnet was f i t t e d by t h i s quartic i E V P U ) = \5.95 — K037xicf 3x ~ h o i ^ x i c r V 1 * 4 - 2 0 Thus the l i n e i n t e g r a l of the f i e l d at a current I and at a constant displacement, x, from the centre l i n e of the magnet i s given . by 600h 400h 200r %-500 0125 0-200 FIGURE 4-12 BEND ANGLE IN MOMENTUM ANALYZING MAGNET 0-275 0-350 RADIANS 102 4 - 2 1 Since the p a r t i c l e s had a curved t r a j e c t o r y , the e f f e c t i v e length was calculated f o r the ho r i z o n t a l displacement at the entrance, e x i t and centre of the magnet. The entrance and ex i t values of x are calculated from the front and back f i t s r e s p e c t i v e l y with z equal to +381 mm from the centre of the magnet. The value of x at z = 0 was used as the average of the intercepts of the front and back tracks. The l i n e i n t e g r a l of the f i e l d used was the weighted average, S B-1< = a k . u s l H d E „ ( v 5 K T R O T C l ) 4 - 2 2 The momentum was corrected f o r energy loss from the centre of the l i q u i d hydrogen target to the downstream side of the S2 counters. A f i t to the range curve f o r CH^ ^ s given by R =r a . G 5 * to~3 T 4 > 23 -2 The t o t a l amount of material was 2.5 g cm The remaining cuts were made to scatte r plots of momentum versus times of f l i g h t . The times of f l i g h t were corrected f o r timing differences to various elements of the hodoscopes used as the TDC stops. The SI to S2 TOF was simply corrected f o r each case of the t r i g g e r - SI to S2A, B, C or D. The SI to S3 TOF was more d i f f i c u l t ; figure 3-2 shows the S3 hodoscope. The counters overlap i n v e r t i c a l p a i r s A-D, B-E and C-F, the G counter overlaps the A-D and the B-E pair s while the H. counter overlaps the B-E and C-F p a i r s . The computer code corrected timing differences f o r each of the sing l e counter stops, a l l of the legitimate 103 two counter coincidences and a l l of the possible three counter coincidences. A scatter p l o t f or the SI to S3 time of f l i g h t versus momentum was made for each of the S2 counters. Deuterons with the same momentum as protons had twice the t r a n s i t time from SI to S3. A two dimensional cut was applied to the scatter p l o t to remove the deuterons. A sample scatter p l o t i s given i n figu r e 4-13, for S2A. The normalized background has been subtracted and the cut i s shown. A very good separation of the protons and the deuterons e x i s t s at a l l momenta. For a t y p i c a l lab. angle of 30 or 40 degrees, the cut removed approximately 2% of the target f u l l data and 8% of the target empty data at 493 MeV, while at 319 MeV i t was 3% of the target f u l l data and 9% of the target empty data. No deuteron production from l i q u i d hydrogen occurs f o r lab angles larger than 10.6 degrees at 493 MeV and 4.8 degrees at 319 MeV. As indicated i n f i g . 4-13, the subtraction of large angle deuterons from the a i r and target canister i s excellent. The s c a t t e r p l o t i n figu r e 4-14 shows the S2 to RF time of f l i g h t versus the momentum for events that f i r e d S2A. The normalized background has been subtracted and the time of f l i g h t has been corrected for the f l i g h t time of the scattered p a r t i c l e where d i s the distance from the centre of the l i q u i d hydrogen target to the S2 counters (2313 mm) and v g i s the v e l o c i t y of the scattered p a r t i c l e , calculated from the measured momentum by 4 r- 24 4 - 25 104 f J *? in* tt » tOJUl • t U T . 1 l I MojtcijON > 3 UJ o • f«,t • 11,0 • »*,0 1«B,0 CUT SI to S3 T o F (channels) Figure 4-13 SCATTER PLOT OF MOMENTUM vs TIME OF FLIGHT OF SCATTERED PROTONS 105 > *1 t* T3 It I 0F t? * COJDTt • « ••RJCCTIIKl UJ ELASTIC PROTONS CUT INELASTIC PROTONS S2 to RF ToF Figure 4 - 1 4 (channels) SCATTER PLOT OF MOMENTUM vs TIME OF FLIGHT OF INCIDENT NEUTRONS 106 where p i s the measured p a r t i c l e momentum and m i s the mass of the s p proton. The S2 to RF time of f l i g h t i s calculated from the SI to RF TOF, SI to S2 TOF's with aligned timing and the f l i g h t time of the scattered p a r t i c l e ; ( SI +o RF TO*) = (Si "To TOF ) 4 - 2 6 — U l \o SX TOT-) + tsc«T This i s the computed time difference between the incident neutron a r r i v i n g at the centre of the l i q u i d hydrogen target and the next RF cycle of the accelerator. The diagonal band of events i n fi g u r e 4-14 are the r e c o i l protons from the slow neutron t a i l of the incident neutron beam energy d i s t r i -bution. The band ends i n the q u a s i - e l a s t i c peak of the f u l l energy neu-trons. Below these events are low momentum protons that were i n e l a s t i c a l l y produced from f u l l energy neutrons by the np—• ppvr" and np —• npTf* reactions. The maximum energy of the i n e l a s t i c protons as a function of lab., angle for the two incident neutron energies i s plo t t e d i n figure 4-15. A cut was imposed on the S2 to RF time of f l i g h t versus momentum scatte r p l o t s to eliminate the i n e l a s t i c protons below t h i s energy. The cut used i s drawn on figu r e 4-14. Above the maximum momentum for i n e l a s t i c s from hydrogen, i n e l a s t i c s from the target f l a s k subtract out. This i s i l l u s t r a t e d i n fi g u r e 4-16, a histogram, plotted on a log scale, of the momentum a f t e r a l l of the cuts have been made plus a +4 ns (+20 channel) cut on the PI to RF TOF to remove the slow neutron t a i l . For angles greater than the maximum angle for i n e l a s t i c proton production, the cut i s located at the largest momentum where the subtraction gives a zero s i g n a l . The cut shown on f i g u r e 4-14 also removes low momentum p a r t i c l e s that have greater RF TOF's than the e l a s t i c protons, supposedly i n d i c a t i n g that 107 4 0 0 DEGREES L A B . FIGURE 4-15 MAXIMUM ENERGY OF INELASTIC NUCLEON COUNTS I 1 1 1 1 1 1 1 1 1 1 1 1 1 r IOOO 10 INELASTIC THRESHOLD loof1* 1 • • . 1 - J I L_ 500 700 900 1100 MOMENTUM MeV/c FIGURE 4-16 MOMENTUM SPECTRUM ( 493 MeV, 10° ) 109 they are f a s t e r . These are the very slow neutrons described i n section 2-1 as being ambiguous i n the RF TOF because t h e i r f l i g h t time was greater than one RF period. After a l l of these cuts, the S2 to RF TOF histogram (with no RF cuts) was printed out f o r each of the S2 counters. A t y p i c a l histogram i s given i n f i g u r e 4-17, where the normalized background has been subtracted. The S2 to RF histograms were also saved i n an array along with the scalers for each run. These histograms were analyzed to y i e l d the d i f f e r e n t i a l cross section a f t e r a l l of the f u l l and empty runs for the angle had been processed through the cuts. The second pass computer code calculated one other set of event by event histograms. These were the s c a t t e r i n g angles for each of the S2 counters. The centre l i n e of the spectrometer was aligned at the back to f i d u c i a l marks on the f l o o r . It was misaligned at the front by an o f f s e t of about 50 mm. The o f f s e t varied with angle so a method of determining the s c a t t e r i n g angle that did not require any knowledge of the o f f s e t was chosen as the most r e l i a b l e and consistent. Figure 4-18 shows two highly s i m p l i f i e d schematics of the plan view of the spectrometer: the f i r s t with the centre l i n e c o l l i n e a r with the nominal s c a t t e r i n g angle, the second with the front of the spectrometer o f f s e t . For the aligned case, the scattering angle, 8 , i s given by e = e„ O M - » t 4 - " where. 0 i s the nominal angle the spectrometer i s set at and 0 i s nom . o r t the angle of the track through, the front x-co-ordlnate MWPC's. This i s no longer true for the second diagram. However the scattering angle, 3 = -0c , 4 - 28 I l l FIGURE 4-18 GEOMETRY USED TO CALCULATE SCATTERING ANGLE 112 can be calculated using the sine law, E C & T where BC i s the distance from the rear cursor of the spectrometer to the S2 s c i n t i l l a t o r s , BT i s the distance from the rear cursor to the centre of the l i q u i d hydrogen target and i s given, i n degrees, by = 1 8 0 - G t — 0A 4 - 3 0 where 8 A i s the angle between the centre l i n e of the spectrometer and the l i n e from the rear cursor to the S2 s c i n t i l l a t o r s . The values of 0^  and BC measured to the centre of the S2 counters were, used as a good approximation to the exact value for each track. The positions of the S2 counters with respect to the centre l i n e of the spectrometer were measured d i r e c t l y and confirmed by reconstructing the s c i n t i l l a t o r p o s i t i o n s using the front wire chamber tracks. For each S2 a histogram of the s c a t t e r i n g angle was printed and stored i n an array along with the S2 to RF TOF's and the s c a l e r s . A t y p i c a l histogram, where the normalized background has been subtracted, i s shown i n fig u r e 4-19. At a p a r t i c u l a r angle and energy, a l l of the f u l l and empty runs were analyzed event by event. The S2 to RF TOF and the s c a t t e r i n g angle histograms f o r each S2 counter and the scalers were saved from each run. The second pass code then calculated the d i f f e r e n t i a l cross section and sc a t t e r i n g angle f o r each of the S2 counters. The number of protons detected was determined by integr a t i n g the RF peak +4 ns (+20 channels) about the centroid channel. The centroid was found by the same method used for the neutron data, The normalized back-ground was subtracted from the target f u l l data and then the weighted mean channel was found between the f u l l width at 10% of the maximum. The 8000 6000 4000 2000 0 MEAN ANGLE 1146° f 1 1 0.0 5.0 D.O 15.0 20.0 DEGREES FIGURE 4-19 CALCULATED SCATTERING ANGLE M 114 Wide Angle Neutron Monitor corrected f o r random vetoes was used for a l l of the normalizations. The d i f f e r e n t i a l cross section was calculated d i r e c t l y from equations 4-15 and 16 rewritten here: dLcT = ^ J I N P \ No 4 - 1 5 £ = No /JL + JL. + J L + J _ ' The f i n a l r e s u l t s were corrected f o r some small systematic e f f e c t s . These e f f e c t s and the f i n a l r e s u l t s w i l l be discussed i n chapter V along with a d e s c r i p t i o n of the error analysis. The s c a t t e r i n g angles were calculated by subtracting the sum of the target empty histograms normalized to the Wide Angle Neutron Monitor from the sum of the f u l l runs. The sc a t t e r i n g angle was computed as the centroid. This angle was corrected f o r systematic e f f e c t s that w i l l be discussed i n chapter V. IV-3. T o t a l Energy Spectrometer The analysis of the t o t a l energy data was s i m i l a r to that of the magnetic spectrometer. It w i l l be discussed here, emphasizing the points that are d i f f e r e n t . The on-line histograms were printed and studied f o r runs with e l e c t r o n i c f a i l u r e s . The f i r s t pass program f i t t e d the tracks i n the front chambers. I t output histograms of: 1) The e f f i c i e n c i e s of the MWPC's. These were the co-ordinates of wires that did not f i r e but were along a track. 2) The reconstruction of the h o r i z o n t a l p r o j e c t i o n of the l i q u i d hydrogen target. 3) The S4 ADC pulse height spectrum. 115 4) The SI to S4 TOF, SI to S2 TOF and the SI to RF TOF. 5) The SI to RF TOF for events that were used to ca l c u l a t e the MWPC ef f i c i e n c y histograms. It also output scatter p l o t s , f o r each of the S2 counters, of the 51 to S2 TOF versus the S4 pulse height and the SI to RF TOF versus the S4 pulse height. The following data was written to proton skim tapes event by event: 1) The b i t pattern i n d i c a t i n g the s c i n t i l l a t o r s that f i r e d . 2) The scalers f o r (CL + CR)•CV, G'CV, the number of events to date, the l i v e time and the r e a l time. 3) The times of f l i g h t started by SI and stopped by S4, S2A, B, C or D and the next RF cycle of the accelerator. 4) The ADC pulse height f o r S4, SI and S2A, B, C or D. F F F F 5) The slope m (m ), intercept a (a ) and the.error on the intercept x y x y O"* 1 for the h o r i z o n t a l ( v e r t i c a l ) f i t to the front chamber data. The proton skim tapes were read by the second pass program. The t o t a l energy second pass code was run f i r s t with a sin g l e f u l l and empty run and no cuts, f o r each of the angles at each energy, The cuts were determined from the outputs of the f i r s t run and the code was run again on a l l of the runs with the cuts discussed here. The b i t pattern was tested to ensure that only one S2 s c i n t i l l a t o r f i r e d per event. This rejected l e s s than 0.1% of the events. The SI to 52 times of f l i g h t peaks were aligned. The tracks were checked to ensure that they came within 20 mm of the outside l i m i t s of the S2 counters. The h o r i z o n t a l tracks were extrapolated back to the l i q u i d hydrogen target. The cuts on the target p r o f i l e eliminated events that otherwise would have subtracted approximately to zero. An upper and lower pulse height cut was made. The l i m i t for large 116 pulse heights was where the background subtraction resulted i n zero for the S4 pulse height spectrum. Figure 4-20 i s an example of an S4 pulse height spectrum. The low pulse height cut was calculated to eliminate pions with the same v e l o c i t y as e l a s t i c a l l y scattered protons. These pions would not be eliminated by the SI to RF TOF cut. The pulse height of p a r t i c l e s In the peak was 1.5 v o l t s and the discriminator threshold was 100 mV. Therefore the zero channel i s 1/15 of the number of channels from peak to threshold below threshold. Figures 4-21 and 4-22 are pl o t s of the ADC channel number versus estimated energy. Five points were plotted: the four peak channels - t h e i r energies c a l -culated from kinematics - and a low energy channel that corresponds to the threshold for the SI to S2 time of f l i g h t . M5 The c a l i b r a t i o n of the ADC for pions should be. more l i k e that of the electron than the proton; hence i t was taken as l i n e a r . The energy of pions with the same v e l o c i t y of e l a s t i c protons i s calculated and the equivalent channel i s read off f i g u r e 4-21 f o r 493 MeV and fi g u r e 4-22 for 319 MeV Incident neutrons. The RF and s c a t t e r i n g angle histograms were printed f or each run and also stored i n a matrix along with the s c a l e r s . After a l l of the target f u l l and target empty runs were analyzed event by event, the d i f f e r e n t i a l cross section and s c a t t e r i n g angle were computed i n an i d e n t i c a l manner to the magnetic spectrometer data. The corrections f o r systematic e f f e c t s to the t o t a l energy data, as w e l l as an error a n a l y s i s , w i l l be discussed i n chapter V. 300 9> 200 CO t-z: ZD O o 00 o o Q 20 o « O O Q ^ Q —o-CP 100 o o C O 200 S 4 Pulse height (chan) FIGURE 4-20 PULSE HEIGHT IN TOTAL ENERGY COUNTER 118 0 0 40 80 120 ENERGY MeV FIGURE 4-21 119 FIGURE 4-22 120 V. Corrections and Systematic Errors Small corrections that compensate for known systematic e f f e c t s are described i n t h i s chapter. Corrections a f f e c t i n g a l l the data w i l l be described f i r s t followed by corrections to the neutron data, the magnetic spectrometer data and the t o t a l energy spectrometer data. Systematic errors w i l l be discussed i n two parts: errors i n the si g n a l and errors i n the normalization. Description of each part w i l l be subdivided as neutron data, magnetic and t o t a l energy spectrometer data. V - l . Target Length The l i q u i d hydrogen target f l a s k was 199.54+.01 mm at 300 K. The c o e f f i c i e n t of expansion was measured on a dummy target to be 1.95 x 10~ 4 + 1.9 x 10~ 6 mmK-1. The dummy f l a s k was 241.35 + .01 mm at 300 K and 240.30 mm at 77 K. Using the c o e f f i c i e n t of expansion, the size of the target f l a s k at 20.76 K i s extrapolated to be 198.5 + .1 mm. V-2. Target Density The density of the l i q u i d para-hydrogen i n equilibrium with i t s vapour i s determined from the pressure. The target was maintained at a pressure of 117 + 1.7 K Pa (17.0 + 0.25 PSIA) corresponding to a tempera-ture of 20.76 K and a density of 70.05 + .4 kg m~3 (0.07005 + 0.0004 -3) gem The density of the para-hydrogen vapour l e f t i n the target f l a s k a f t e r i t was emptied depends on both the temperature and the pressure. The pressure remained at 117 +1-7 kPa and the temperature was measured by three copper-constantan thermocouples connected to a chart recorder. As the thermocouple junctions not i n the target were at room temperature, the target f u l l periods were used as baselines. The change i n emf was 0.25 +0.1 mV when the target was emptied. The temperature of the. 121 "target empty" para-hydrogen gas was therefore 48 + 8K. The density of -3 -4 -3 the vapour was 0.54 + 0.2 kgm (5.4 x 10 gem ). The d i f f e r e n t i a l cross section formulae corrected f o r the gas i n the empty target becomes icr = R | NF _ N M T \ \ <LQ, 5 - 1 where p ^ i s the density of l i q u i d para-hydrogen and p ^ i s the density of para-hydrogen vapour. The differ e n c e (^-^ PQ* ^ s e ( 3 u a l - t o 69.51 + 0.4 kgm"3 (0.06951 + .004 gem" 3). V-3. Neutron Beam Attenuation The neutron beam incident on the l i q u i d hydrogen target i s attenuated as i t passes through the LH^. Therefore, target protons "see" a d i f f e r e n t number of incident neutrons depending on t h e i r p o s i t i o n i n the target. The incident f l u x i s the average given by the equation. ? where t i s the length of the target and O" i s the neutron-nroton t o t a l np cross section. With the values f o r the t o t a l cross section discussed i n chapter 6, the average beam f l u x i s 0.9850 + 0.0001 of the incident beam fl u x . The error i s calculated from the error on the t o t a l cross section. V-4. Corrections to the Neutron Signal Several small corrections were made to the r e s u l t s of the forward neutron experiment. The neutron s i g n a l was corrected f o r attenuation, double s c a t t e r i n g , d i f f r a c t i o n s c a t t e r i n g , i n e l a s t i c s , time of f l i g h t "wrap around" and "sky-shine". The average s o l i d angle and the geo-metric s c a t t e r i n g angle were calculated as well. 122 Scattered neutrons were attenuated by the l i q u i d hydrogen i n the target, the mylar target f l a s k s , the aluminum vacuum ve s s e l and the a i r between the target and the detector. The d i f f e r e n t i a l cross section f o r sc a t t e r i n g from a n u c l e i outside of the d i f f r a c t i o n peak was estimated to be equal to the nucleon-nucleon cross section f o r n-p sc a t t e r i n g plus n-n or pp sc a t t e r i n g m u l t i p l i e d by the area of the nucleus. Therefore, the number of p a r t i c l e s scattered from a nucleus at an angle 8 i s • N,te>a KUt( ffUgv, + fl^ifTm \ 5 - 3 where N q i s Avogadro's number, t i s the length of target material, p i s 2/3 i t s density, A i s the number of nucleons per n u c l e i (A i s proport-i o n a l to the area of the nucleus) and dc/dil i s the nucleon-nucleon d i f f e r e n t i a l cross section. The d i f f r a c t i o n peak i s approximated by 5 - 4 where J^(x) i s a f i r s t order Bessel function and k i s the momentum -k = \\ p. The detected rate of neutrons i s corrected by 5 - 5 However, t h i s over compensates because some of the scattered neutrons are s t i l l within the acceptance of the detector. This c o r r e c t i o n i s given by v T r x « r ax*. 123 where A-Q. i s the s o l i d angle of the detector from the target. The attenuation of the neutron beam detected at zero degrees i s calculated i n exactly the same way and y i e l d s an expression s i m i l a r to 5-6. The d i f f e r e n t i a l cross section was m u l t i p l i e d by the cor r e c t i o n f o r the s i g n a l and divided by the zero degree correction. The calculated corrections (approximately 1% to 3%) at 319 and 493 MeV are l i s t e d i n table 5-1 as a function of energy. The errors f o r the nuclear attenuation c a l c u l a t i o n were 20% for the uncertainty on the t o t a l cross sections and 2.5% for the error on the track length through the LIL^. There i s a small p r o b a b i l i t y that a p a r t i c l e scattered once w i l l s catter again. I f the f i r s t s c a t t e r was directed towards the detector a second scatt e r may cause i t to miss and vice-versa. The kinematic quantities f o r double sc a t t e r i n g are shown i n fig u r e 5-1. The p r o b a b i l i t y of a sin g l e s c a t t e r i n t o the detector i s given by The p r o b a b i l i t y of a p a r t i c l e s c a t t e r i n g with polar angles (8^,4>^) i s given by LNoP do-K . e P c L U o s ^ * ) dlft, 5 - s where 0 ^* i s the scattering angle 0 ^ (lab.) i n the centre of mass. The p r o b a b i l i t y of a second scatter i n t o the detector i s given by {'No/? d 0 - ( T t, 9 x ) A J I L M d-QcMUtA*) 5 - 9 where T^ i s the energy of the p a r t i c l e a f t e r the f i r s t s c a t t e r . The correction to the data i s the p r o b a b i l i t y of a double scatter divided by the p r o b a b i l i t y of a sing l e scatter TABLE 5-1 Attenuation and Double Scattering Correction f o r Neutrons 319 MeV .M. Scattering Attenuation Double Angle Scattering Degrees Percent Percent 10. 1.849 -.574 20. 1.836 -.630 30. 1.817 -.675 40. 1.798 -.922 50. 1.783 -.772 60. 1.785 -.825 70. 1.815 -.889 80. 1.892 -.962 90. 2.040 -1.'079 493 MeV 10. 1.826 -.621 20. 1.802 -.684 30. 1.763 -.719 40. 1.713 -.756 50. 1.655 -.796 60. 1.595 -.838 70. 1.553 -.883 80. 1.542 -.922 90. 1.572 -.957 125 FIGURE 5-1 KINEMATICS OF DOUBLE SCATTERING 126 do-IT . .e . l <JHL*(e»,-hf) 5 " 1 1 d i l d . . Q u l ^ e . , 0 where K(L, T q , 8 ^ ; l ' , Tj_'®2^ represents the kinematic l i m i t s imposed by the range of the p a r t i c l e and the acceptance of the detector with respect to energy and angle. The r e s u l t s of the c a l c u l a t i o n f o r the double s c a t t e r i n g c o r r e c t i o n at 319 and 493 are l i s t e d i n table 5-1 as a function of angle. The e f f e c t i s of the order of 1%. The error on the double s c a t t e r i n g c a l c u l a t i o n was estimated to be 27%, due to uncer-t a i n t i e s i n the d i f f e r e n t i a l cross section. D i f f r a c t i o n s c a t t e r i n g of the neutron beam produces a background at small angles i n the lab. This background does not subtract completely because the f u l l l i q u i d hydrogen target attenuates neutrons that have scattered upstream and attenuates the incident neutron beam that sub-sequently scatters downstream. A c a l c u l a t i o n based on equation 5-4 f i t s the shape of the measured background to s i g n a l r a t i o very w e l l . The normalization i s taken from the data. The correction at 319 MeV i s given i n table 5-2, at 493 MeV the correction i s n e g l i g i b l e . The uncer-ta i n t y i n the c a l c u l a t i o n was estimated as the standard deviation of a square d i s t r i b u t i o n 50% of the correction wide. The errors are tabulated with the r e s u l t s . The +4 ns cut on the PI to RF TOF did not exclude some i n e l a s t i c neutrons f rom np—> nnfT + and np—>np1T° reactions. The reaction cross section f o r t h i s i s i n s i g n i f i c a n t at 319 MeV but i s about 1 mb at 493 MeV^. The i n e l a s t i c reactions are assumed to be I = 1 from the isobar model. Thus, the reactions are forward-backward peaked and symmetric TABLE 5-2 D i f f r a c t i o n Scattering Correction f o r Neutrons 319 MeV Lab. Correction Angle Degrees mb 5.0 0.269 ± 0.155 7.5 0.114 ± 0.065 15.0 0.013 ± 0.008 22.5 0.0 TABLE 5-3 Correction to Neutron Data for I n e l a s t i c Events 493 MeV Lab. Correction Angle Degrees mb 2.5 0.038 5.0 0.035 7.5 0.03.0 10.0 0.0.24 12.5 0.017 15.0 0.010 17.5 0.004 128 about 90 degrees i n the centre of mass. A phase space d i s t r i b u t i o n m u l t i p l i e d by {. \ + P^co&e, 1 \. ) -V jpt oo S^GJL. \ 5 - 1 1 where p Q i s the incident neutron mementum, p^ and are the scattered nucleon momenta and & ^ and 6 ^ a r e the respective s c a t t e r i n g angles, y i e l d s the corrections l i s t e d i n table 5-3. The errors on these corrections were estimated as 25% for the TOF cut and 25% for the phase space approximation. Added i n quadrature t h i s gave a 35% t o t a l error. Wrap around neutrons r e f e r to very slow neutrons that have a TOF greater than the RF period. Data taken with 43 ns and 215 ns beam r e p e t i t i o n rates were analyzed separately and t h e i r signals compared. There was no s t a t i s t i c a l l y s i g n i f i c a n t e f f e c t at the one standard deviation l e v e l . A measurement was made of the neutrons scattered from material around the detector. A 0.914 m t h i c k by 0.610 m wide by 0.305 m block of s t e e l (shadow bar) was mounted between the l i q u i d hydrogen target and the neutron detector. Data was taken for the same time as a t y p i c a l run. The f u l l minus empty spectra showed no s i g n a l at the 10% l e v e l . This agrees with the double s c a t t e r i n g correction of a maximum of 1%. The s o l i d angle c a l c u l a t i o n discussed i n chapter IV assumed a point source of neutrons at the centre of the l i q u i d hydrogen target. The correct s o l i d angle i s the average over the hydrogen target weighted by the d i s t r i b u t i o n of the incident neutrons throughout the target. For ease of c a l c u l a t i o n the weight was set to unity and an order of magni-tude c a l c u l a t i o n was made. A numerical evaluation, by four point Gaussian quadrature with two i n t e r v a l s per i n t e g r a t i o n was made of the following i n t e g r a l , 129 5 - 1 2 where ,p , z) are c y l i n d r i c a l polar co-ordinates of a point i n the LH^ target, r i s the radius of the target and L i s the length, (x » y Q , z ) are cart e s i a n co-ordinates - with the o r i g i n at the centre of the detector - of the point ,p, z ) , x^, x^, y^, y^ are the boundaries of the detector and Xi i s the expression for the s o l i d angle given i n equation 4-12. The cor r e c t i o n i s less than 0.1% and has been neglected. The s c a t t e r i n g angle of the neutrons i s the average of the angle between the d i r e c t i o n of the beam and the l i n e connecting the i n t e r a c t i o n point i n the target with the conversion point i n the carbon weighted by the d i s t r i b u t i o n of neutrons i n the target. A four point Gaussian qua-drature with two i n t e r v a l s per in t e g r a t i o n was made of the following expression at each nominal s c a t t e r i n g angle *v T rx» <\Y» where P i s the beam p r o f i l e calculated from the zero degree wire chamber reconstruction of the beam, A i s the attenuation of the neutron beam as i t traverses the target and 8 i s the sca t t e r i n g angle. The •'. log of the beam profile was f i t t e d with a polynomial top and Gaussian wings. The attenuation was given by the measured t o t a l cross sections described i n Chapter 6. The nominal s c a t t e r i n g angle i n the lab, the nominal centre of mass sca t t e r i n g angle and the average CM. sca t t e r i n g angle are l i s t e d 130 in table 5-4 for 319 and 493 MeV. The error on the scattering angle was estimated to be +0.05 degrees. V-5. Corrections to Zero Degree Data Two corrections were made to the zero degree data, f i r s t the attenuation by the LH^ and second the background i n the nuetron monitors. Data c o l l e c t e d at zero degrees with the LH^ target f u l l were corrected by en t C " n P w h e r e - xVio0 " t / l f l » the number of protons per unit area and * I u M x n~ i s the neutron - proton t o t a l cross section. w n p The "In Beam" and "Wide Angle" Nuetron Monitors had a nonzero rate of 0.470 counts per second at 319 MeV and 0.666 counts per second at 493 MeV when the neutron beam was turned o f f . This rate was an i n s i g n i f i c a n t e f f e c t at primary proton beam currents of 100 to 500 nA when the detector was at nonzero angles but this' background correction was important at the 1 to 2 nA proton currents i n use when the detector was at zero degrees. The background rate was due to a c t i v a t i o n of the s c i n t i l l a t o r s , the collimators and the magnet near them. The l i n e a r i t y of the monitor res-ponse was not affected by the incident neutron rate. Figure 5-2 i s a plo t of the [CL + CR]*CV rate versus the L+R rate - the primary proton beam monitor rate - f or zero degree runs at 493 MeV. V-6. Corrections to E f f i c i e n c y Measurements The e f f i c i e n c y measurement was corrected for proton and neutron attenuation and double s c a t t e r i n g . The r e s u l t s , reported i n R. Dubois' D2 thesis , are approximately a 2 to 3% corr e c t i o n . The e f f i c i e n c y r e s u l t s reported i n chapter IV have t h i s c orrection already incorporated. V-7. Corrections to Proton Data-Magnetic Spectrometer The magnetic spectrometer data was corrected for attenuation, double s c a t t e r i n g , d i f f r a c t i o n and average s o l i d angle. The sca t t e r i n g angle was corrected to the average of the geometric angle. The TABLE 5-4 Corrected Scattering Angles f or Neutrons 319 MeV Nominal Nominal Corrected Lab. CM. CM. Angle Angle Angle Degrees Degrees Degrees 5.0 10.812 11.130 7.5 16.210 16.418 10.0 21.597 21.751 15.0 32.328 32.428 22.5 48.270 48.334 30.0 63.971 64.016 39.5 83.446 83.476 45.0 94.495 94.519 •493 MeV 7.5 16.840 17.056 10.0 22.427 22.591 12.5 27.993 28.122 22.5 49.949 50.009 30.0 65.989 66.029 45.0 96.737 96.747 133 attenuation and double s c a t t e r i n g corrections at 319 and 493 MeV are l i s t e d i n table 5-5 as a function of CM. angle. For very low energy protons, d i f f r a c t i o n s c a ttering becomes s i g n i -f i c a n t . The calculated c o r r e c t i o n as a function of energy, given i n table 5-6 for the SI and S2 s c i n t i l l a t o r s , are of the order of 1%. The s o l i d angle correction f o r the proton data was calculated as i t was for the neutron data. In t h i s case the correction was l e s s than 0.12% f or a l l angles and consequently was neglected. The sc a t t e r i n g angle correction f o r the proton data was more compli-cated than f o r the neutron data. As described i n chapter IV, the proton s c a t t e r i n g angle was calculated as the centroid of the histogram of the angle computed from the h o r i z o n t a l MWPC tracks. The centroid i s written as osr r \_ x, v, where dcr/dSl. is~ the n-p d i f f e r e n t i a l cross section, Is the Jacobian and 8 i s the h o r i z o n t a l p r o j e c t i o n of the sca t t e r i n g angle between the neutron beam axis and a l i n e connecting a point (^ ,p , z) i n the LTL^  target to a point (x, y, z ) on the detector. The expression 5-14 was evaluated by four point Gaussian quadrature with, two i n t e r v a l s per in t e g r a t i o n f o r a range of nominal angles (the angle between the d i r e c t i o n of the beam and the l i n e connecting the centre of the LH^ target with, the centre of an S2 s c i n t i l l a t o r ) . The average scattering angle,< 9^ , was calculated from equation 5-13 for the same nominal angles. Table 5-7 l i s t s the nominal s c a t t e r i n g angle, the 134 TABLE 5-5 Attenuation and Double Scattering Corrections for Protons - Magnetic Spectrometer 319 MeV CM. Scattering Angle Degrees Attenuation Percent Double Scattering Percent 180. 2.067 -0.468 170. 2.063 -0.671 160. 2.052 -0.927 150. 2.037 -1.132 140. 2.019 -1.404 130. 2.002 -1.434 120. 1.993 -1.782 110. 2.000 -2.209 100. 2.032 -2.617 90. 2.106 -2.867 80. 2.271 -3.001 70. 2.636 -3.066 60. 3.392 -3.303 50. 4.960 -3.906 493 MeV 180. 2.484 -0.348 170. 2.466 -0.593 160. 2.414 -0.833 150. 2.330 -1.047 140. 2.219 -1.284 130. 2.089 -1.664 120. 1.948 -2.184 110. 1.860 -2.732 100. 1.845 -2.985 90. 1.853 -2.194 80. 1.902 -2.101 70. 2.020 -1.988 60. 2.316 -1.995 50. 3.059 -2.217 40. 4.922 -2.840 TABLE 5-6 D i f f r a c t i o n Scattering Correction f o r Protons K i n e t i c Correction f o r Correction f o r Energy SI Counter S2 Counter MeV Percent Percent 136. 0.071 0.109 100. 0.204 0.227 49. 0.995 0.638 40. 1.141 0.712 30.3 1.638 0.755 136 TABLE 5-7 Scattering Angle Corrections f o r Proton Data 319 MeV Nominal Lab Angle Degrees 0. 1. 2. 3. 4. 5. 10. 20. 30. 40. 50. 60. 70. <9P> Degrees 0.359 0.987 1.985 2.985 3.985 4.985 9.986 19.982 29.966 39.973 50.021 60.010 69.956 <e> Degrees 0.577 1.111 2.054 3.036 4.028 5.023 10.014 20.011 30.011 40.010 50.008 60.005 70.000 <e%> Degrees 179.224 177.864 175.706 173.544 171.381 169.139 158.373 136.996 116.005 95.521 75.586 56.172 37.194 <9*> <©*,> Degrees 0.9974 0.9985 0.9992 0.9994 0.9995 0.9995 0.9996 0.9996 0.9992 1.9992 1.0003 0.1002 0.9978 493 MeV 0. 1. 2. 3. 4. 5. 10. 20. 30. 40. 50. 60. 70. 0.354 0.973 1.971 2.973 3.976 4.978 9.986 19.970 29.967 40.014 50.021 60.016 69.963 0.577 1.111 .054 .036 ,028 .023 2. 3. 4. 5. 10.014 20.011 30.011 40.011 50.008 60.005 70.000 179.204 177.813 175.572 173.321 171.071 168.822 157.622 135.585 114.132 93.350 73.471 54.367 35.970 0.99.72 0.9983 0.9989 0.9992 0.9993 0.9994 0.9996 0.9993 0.9992 1.0001 1.0003 1.0004 1.9981 137 average h o r i z o n t a l p r o j e c t i o n of the scattering angle and the average s c a t t e r i n g angle. The angle calculated by the analysis i s < S p V "whereas the correct angle i s . To f a c i l i t a t e the corrections table 5-7 also l i s t s < e £ > and <9*> for each nominal s c a t t e r i n g angle where (©*p> i s the average h o r i z o n t a l p r o j e c t i o n of the sca t t e r i n g angle transformed to the CM. and <6*^ i s the average s c a t t e r i n g angle transformed to the CM. Thus multip l y i n g the value of calculated by the analysis program by the corresponding value of <9*> / < 9 * ^ y i e l d s the corrected centre of mass sc a t t e r i n g angle. V-8. Corrections to Proton Data - Total Energy Spectrometer The t o t a l energy spectrometer data was corrected i n the same way as the magnetic spectrometer data. The corrections for attenuation and double s c a t t e r i n g are l i s t e d i n table 5-8. The s o l i d angle c a l c u l a t i o n was i d e n t i c a l and was neglected. The scat t e r i n g angle was corrected exactly as for the momentum analyzed data; the r e s u l t s given i n table 5-7 are s t i l l a p plicable. The d i f f r a c t i o n s c attering c a l c u l a t i o n f o r the SI s c i n t i l l a t o r i s d i r e c t l y applicable to the t o t a l energy data. The corrections are l i s t e d In table 5-6. A co r r e c t i o n f o r the i n t e r a c t i o n t a i l , a r i s i n g when energetic pro-tons are stopped i n a detector, was calculated. A f r a c t i o n of th i s t a i l was cut o f f to eliminate pions with the same v e l o c i t y as e l a s t l c a l l y scattered protons. The t a l l shape was not known so a l i n e a r decline to zero was chosen. The slope was calculated from the f r a c t i o n of i n t e r -M6 acting protons given the average incident proton energy and the c a l -culated energy of the cut. The contribution of the missing t a i l was integrated and the f r a c t i o n a l correction i s l i s t e d i n table 5—9.. The primary source of error i s the unknown t a i l shape. A f l a t t a i l (an TABLE 5-8 Attenuation and Double Scattering Corrections for Protons - To t a l Energy Spectrometer 319 MeV CM. Scattering Attenuation Double Angle Scattering Degrees Percent Percent 80. 1.629 -3.001 70. 1,877 -3.066 60. 2.424 -3.303 50. 3.559 -3.906 493 MeV 80. 1.372 -2.101 70. 1.440 -1.988 60. 1.639 -1.995 50. 2.169 -2.217 40. 3.515 -2.840 TABLE 5-9 Correction f o r Interaction T a i l for Total Energy Spectrometer Data 319 MeV S2 Scattering Interaction T a i l S c i n t i l l a t o r Angle (Lab.) Correction Degrees Percent S2A 54.55 0.72 S2B 53.57 0.66 S2C 52.62 0.65 S2D 51.69 0.58 493 MeV S2A 58.3 0.59 S2B 57.3 0.60 S2C 56.4 0.64 S2D 55.4 0.65 140 extreme case) would add as much as 50% to the correction. Therefore, a middle value of 30% was estimated as the error. V-9. Error Analysis f o r the Neutron Signal The systematic errors are described here. The e f f e c t of cuts on the data was studied by varying the cuts and computing the change i n the d i f f e r e n t i a l cross section. Where there were several measurements of the same quantity the variance and % were calculated. The systematic errors on the s i g n a l for the neutron data and then the proton data w i l l be discussed, followed by estimates of the error on the normalization of the data. Four cuts were made to the neutron data. The PI to P2 TOF cut shown i n f i g u r e 4-1 was v a r i e d i n 1.0 ns (5 channel) steps towards the neutron peak. Figure 5-3 shows the s i g n a l , at 319 and 493 MeV, as a function of the change i n the cut normalized to the f u l l s i g n a l . The estimated error was 0.69% at 493 MeV and 0.25% at 319 MeV. The +200 mm cut on the v e r t i c a l and h o r i z o n t a l intercept of the reconstructed tracks i n the neutron detector was reduced i n 25 mm steps. The calculated s i g n a l divided by the s o l i d angle i s p l o t t e d i n f i g u r e 5-4 f o r the 319 and 493 MeV data as a function of carbon cut. The error, estimated as 2.12% and 0.65% at 319 and 493 MeV r e s p e c t i v e l y , was calcu-lated as the d i f f e r e n c e between the average s i g n a l over a l l of the cuts and the s i g n a l used i n the a n a l y s i s . The e f f e c t was predominately due CI to the loss of chamber e f f i c i e n c y near the support wires The cut on the s c a t t e r i n g angle In the carbon was v a r i e d . The maxi-mum angle was set by geometry so the 17° cut was compared with 16° and 15°. The Invariant quantity studied was No v,. VARIATION IN NEUTRON SIGNAL WITH PI TO P2 TOF CUT •Oh 319 MeV 0.9 h _L 165 175 185 CHANNEL o 1.005 CO 493 MeV UJ o < o 1.00 f -± l$0 170 180 CHANNEL FIGURE 5-3 Fractional change in the differential cross section as the cut on the PI to P2 T O F is varied . 142 10 - . 8 2 •80 •78 •76 •74 •72 C; -70 O o < -128 o to •126 •124 •122 •120 •118 •116 T 1 1—r "i 1 1 1 1 1 1 1 1 r-319 MeV H—h I I I—•—I—I—I—I—I—I—I I I I—I—I—I—h 4 9 3 MeV • • 50 100 i I i i • • • 150 200 mm Figure 5 - 4 VARIATION IN SIGNAL A S A FUNCTION OF C A R B O N C U T The signal is normalized to the solid angle corresponding to the area of the carbon remaining . 1 4 3 where N i s the rate of the s i g n a l , N i s the rate at zero degrees,r> 0 s o v i s the e f f i c i e n c y at the beam energy and i s the e f f i c i e n c y at the energy of the scattered neutrons. Each of these were recalculated with the ©c cut equal to 1 6 ° and 1 5 ° . The e f f i c i e n c i e s were recalculated D 2 following the procedure outlined i n R. Dubois' thesis . The v a r i a t i o n was 0 . 1 0 % at 3 1 9 MeV and 0 . 1 7 % at 4 9 3 MeV. The PI to RF TOF cut f o r slow neutrons was varied by + . 4 ns (+ 2 channels). The percent change i n the s i g n a l was 0 . 3 8 % at 3 1 9 MeV and 0 . 4 0 % at 4 9 3 MeV. The forward d i f f e r e n t i a l cross section measurement depends on the r a t i o of the e f f i c i e n c i e s , / 1£ $ . Three sources of error i n t h i s r a t i o were studied, the s t a t i s t i c a l error on the measurement of / > the error on the energy of the incident neutrons and the v a r i a t i o n i n the e f f i c i e n c y i f d i f f e r e n t functions were chosen f or the f i t . Because the error on and are correlated, the s t a t i s t i c a l error on the r a t i o was calculated from the f u l l error matrix for the f i t . If the r a t i o i s written as g. = vfh-o) = fl. » fl./ To T ft jTo* + Fj3 /To3 5 _ 1 6 where A_. are the parameters of the f i t given i n chapter 4 (equation 4 - 1 3 ) T q i s the energy of the beam, T^ i s the energy of the scattered neutrons. The error on £ i s given by F JL °l = A. f* [J* \\-Al- \ or.. 5 _ 1 7 where CT .. i s the error matrix given i n table 4 - 1 . Table 5 - 1 Q Is a l i s t of the e f f i c i e n c y r a t i o and the t o t a l s t a t i s t i c a l error 0\ for each lab angle at 3 1 9 MeV and 4 9 3 MeV r e s p e c t i v e l y . The r a t i o £ depends on T and T . T.. was calculated from T by o s s o TABLE 5-10 E f f i c i e n c y Ratio and T o t a l S t a t i s t i c a l Error for Each Lab. Angle at 319 MeV and 493 MeV Lab Angle Degrees 5.0 7.5 15.0 22.5 29.5 35.0 45.0 319 MeV Ratio of E f f i c i e n c y at the Scattering Angle to E f f i -ciency at Zero Degrees  1.0066 1.0149 1.0624 1.1522 1.2938 1.4755 2.5704 Total S t a t i s t i c a l Error ±.0002 ±.0005 ±.0022 +.0067 ±.0177 ±.0369 ±.0959 7.5 10.0 12.5 22.5 30.0 45.0 493 MeV 1.0118 1.0213 1.0337 1.1207 1.2416 1.8096 ±.0006 ±.0012 ±.0018 ±.0061 ±.01077 ±.03452 145 -I ' / T MeV"' xlO~ Figure 5-5 EFFICIENCY FITTED WITH VARIOUS FUNCTIONS 146 r e l a t i v i s t i c kinematics. The value of T was var i e d by +2 MeV and the o — average percent d i f f e r e n c e , x e l " r 0 > T s C T . ) ) was calculated and tabulated i n table 5 - 1 0 . A comprehensive study of the s e n s i t i v i t y of the e f f i c i e n c y to the choice of the f i t function was performed. Figure 5-5 i s a p l o t of the e f f i c i e n c y as a function of 1/T. The s o l i d curves are l i n e a r , quadratic, and cubic f i t s i n 1/T and 1/p where p i s the momentum of the neutron. The e f f i c i e n c y r a t i o was calculated at T g = 450, 400, 350, 319, 250 and 200 MeV for T = 493 MeV and at T = 250, 200 and 150 f o r T = 319 MeV o s o for each of the s i x f i t s . The average over a l l of the f i t s , less the worst one, of the r a t i o was calculated. The "X.X per point for f i v e points was approximately one i n every case. The percent uncertainty i n the e f f i c i e n c y due to the choice of the fu n c t i o n a l dependence of the f i t was approximated by the standard deviation of the average divided by the average. The error on the r a t i o at the measured scattered neutron energies were interpolated and are l i s t e d i n table 5-10. The s t a b i l i t y of the neutron monitor - [CL + CR] • GV - used i n t h i s analysis was studied against the "In Beam" Neutron Monitor. Figures 5-6 and 5-7 show the r a t i o of [CL + CR]•CV + [CL + CR]-CV-CV , the "Wide Angle" Neutron Monitor, to G-CV + G-CV-CV , the "In Beam" Neutron Monitor, versus run number for both the neutron and proton data at 319 and 493 MeV re s p e c t i v e l y . The percent error was computed as the standard deviation divided by the average. For the neutron runs i t i s equal to 0.2% at 319 MeV and 3.84% at 493 MeV. At most angles there were several runs of both target f u l l and empty data. As described i n chapter IV, these were grouped into RATIO OF IN BEAM MONITOR TO WIDE ANGLE MONITOR AT 319 MeV T—i r RATIO 8.0 NEUTRON PROTON 7.5 - I 1 1 I L 290 350 1 i i_ 1000 1060 850 RUN NUMBER FIGURE 5-6 The stability of the neutron beam monitors was calculated as the standard deviation of the ratio plotted here . RATIO OF IN BEAM MONITOR TO WIDE ANGLE MONITOR AT 493 MeV RATIO 18.0 N E U T R O N P R O T O N 17.0 • • ' L _ _ _ l 1 1_ 1 1 • i I • i — i 1 1 1 J — i i — — — ' 1 1 1— 1 1 1 1 1 1 1 1 I • » • I 60 100 140 700 740 1090 1140 1320 1360 RUN NUMBER FIGURE 5-7 The stability of the neutron beam monitors was calculated as the standard deviation of the standard deviation of the ratio plotted here 149 sequential runs that gave a "X9, per point of one for both f u l l and empty data. The s i g n a l from each of these groups was averaged to give the f i n a l s i g n a l and i n every case the 2 J a per point was close to one. There-fore, no a d d i t i o n a l error was required to-guarantee the s t a t i s t i c a l r e p r o d u c i b i l i t y of the data. The f i n a l errors discussed here f or the neutron analysis are those on the calculated corrections. They were discussed along with each, corr e c t i o n . The t o t a l error f o r the double s c a t t e r i n g and attenuation c o r r e c t i o n was 33.6%. The percent error on the d i f f e r e n t i a l cross section i s given by 6& — 0.33(> ? 5 - 1 9 c c where C i s cor r e c t i o n factor f o r do - /dSL , (C = 1 + f) and f i s the tabulated correction. Table 5-11 summarizes the errors at each lab angle f o r both energies. The t o t a l r e l a t i v e error i s obtained by adding a l l of the errors i n quadrature. M u l t i p l y i n g the t o t a l r e l a t i v e error by the d i f f e r e n t i a l cross section y i e l d s the t o t a l absolute error. V-10. Error Analysis of the Proton Signal - Magnetic Spectrometer The error analysis f o r the magnetic spectrometer data was simpler than f o r the forward neutron data. The only s i g n i f i c a n t cut that was not based on a subtraction was the f i n a l RF cut. The other cuts, described i n chapter IV were applied where the s i g n a l subtracted to zero. Thus, small changes i n the cut made i n s i g n f i c a n t changes In the s i g n a l and were neglected. The r e p r o d u c i b i l i t y of the proton data was determined by comparing measurements i n the same angular range that were taken at d i f f e r e n t TABLE 5-11 Summary of Errors on Neutron Signal 319 MeV Percent Error Frbm\Lab. Angle 5. 0 7. 5 15 i.O 22 :.5 29 1.5 35 i.O 45 i.O S t a t i s t i c s 5. 99 2. 06 1. 38 0. 94 1. 51 1. 52 6. 58 I n e l a s t i c s Correction 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 D i f f r a c t i o n 3. 11 1. 33 0. 20 0. 0 0. 0 0. 0 0. 0 Double Scattering and Attenuation 0. 42 0. 41 0. 38 0. 34 0. 31 0. 31 0. 33 E f f i c i e n c y S t a t i s t i c s 0. 02 0. 05 0. 21 0. 59 1. 37 2. 50 3. 73 RF Cut 0. 40 0. 11 0. 20 0. 52 0. 02 0. 23 0. 20 Monitor S t a b i l i t y 0. 20 0. 20 0. 20 0. 20 0. 20 0. 20 0. 20 Target Attenuation 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 0. 01 Energy Uncertainty 0. 00 0. 00 0. 01 0. 04 0. 08 0. 17 1. 42 Carbon Cut 2. 12 2. 12 2. 12 2. 12 2. 12 2. 12 2. 12 E f f i c i e n c y F i t t i n g Function 0. 10 0. 20 0. 40 0. 50 1. 90 3. 60 5. 60 PI to P2 TOF Cut 0. 25 0. 25 0. 25 0. 25 0. 25 0. 25 0. 25 Carbon Scattering Angle 0. 10 0. 10 0. 10 0. 10 0. 10 0. 10 0. 10 493 MeV Percent \ Error From\ Lab. Angle 7. .5 1C 1.0 12 :.5;. 22 :.5 30.0 45 i.O S t a t i s t i c s 2. .52 1. 85 1. 70 1. 06 1. 45 3. 89 I n e l a s t i c Correction 0. .19 0. 16 0. 13 0. 0 0. 0 0. 0 D i f f r a c t i o n 0. ,0 0. 0 0. 0 0. 0 0. 0 0. 0 Double Scattering and Attenuation 0. .40 0. 39 0. 35 0. 28 0. 24 0. 20 E f f i c i e n c y S t a t i s t i c s 0. .06 0. 11 0. 18 0. 54 0. 87 1. 91 RF Cut 1. ,25 1. 93 0. 21 0. 49 0. 24 0. 72 Monitor S t a b i l i t y 3. .84 3. 84 3. 84 3. 84 3. 84 3. 84 Target Attenuation 0. .01 0. 01 0. 01 0. 01 0. 01 0. 01 Energy Uncertainty 0. .00 0. 00 0. 00 0. 03 0. 05 0. 13 Carbon Cut 0. .65 0. 65 0. 65 0. 65 0. 65 0. 65 E f f i c i e n c y F i t t i n g Function 0. .30 0. 40 0. 45 1. 03 1. 41 2. 20 PI to P2 TOF Cut 0. ,69 0. 69 0. 69 0. 69 0. 69 0. 69 Carbon Scattering Angle 0. ,17 0. 17 0. 17 0. 17 0. 17 0. 17 151 times. At 319 MeV, there were two data sets (4 points each) i n the range between 127 and 135 degrees and between 149 and 156 degrees i n the centre of mass. The eight points of the overlapping data sets were f i t t e d by a least squares f i t to a l i n e . For the two angular ranges the "X. 2 per data point was 1.2 and 0.33. The larger X /n was used to determine the r e p r o d u c i b i l i t y error; as the average error was 1.5% a r e p r o d u c i b i l i t y error of 0.67% increases the average error by "X. /n . There were three overlapping data sets (4 points each) at 493 MeV i n the angular range from 84 to 93 degrees i n the centre of mass. The 2 twelve points were f i t by a l i n e and the X was 26.4. One point con-2 2 t r i b u t e d a p a r t i a l X of 7.8 and was rejected reducing the % to 18.62 f o r 11 points. The r e p r o d u c i b i l i t y error to be added i n quadrature was calculated as 1.23%. The errors on the calculated corrections were previously discussed. Table 5-12 summarizes a l l of the errors that remain constant with respect to angle and table 5-13 l i s t s the errors calculated for each data point. V - l l . Error Analysis of the Proton Signal -Total Energy Spectrometer A l l of the errors calculated f o r the magnetic spectrometer data apply to the t o t a l energy data as w e l l as the error on the correction for the i n t e r a c t i o n t a i l . Table 5-14 l i s t s a l l of the errors for the t o t a l energy data. V-12. Normalization Error The normalization of the neutron data i s given by MCO°) 5 - 20 NU") n t where N(0°)/MC0°) i s the number of neutrons detected at zero degrees per monitor count and n i s the number of protons per unit area i n the target. TABLE 5-12 Summary of Angle Independent Errors on Proton Signal Description 319 MeV 493 MeV Target Attenuation 0.01% 0.01% RF Cut 0.53% 0.69% Monitor S t a b i l i t y 0.35% 0.32% Re p r o d u c i b i l i t y 0.67% 1.23% 153 FIGURE 5-13 Summary of Errors on Proton Signal 319 MeV C.M. S t a t i s t i c a l Double Scattering D i f f r a c t Angle Error and Attenuation Deg. % % % 66.73 0.92 0.09 0.28 68.62 0.89 0.12 0.28 70.47 0.92 0.15 0.27 72.33 0.90 0.17 0.26 76.59 1.02 0.22 0.26 78.40 0.99 0.24 0.26 80.33 1.02 0.25 0.26 82.26 1.01 0.26 0.26 86.62 1.37 0.26 0.00 88.45 1.32 0.26 0.00 90.29 1.34 0.26 0.00 92.26 1.35 0.25 0.00 96.55 1.01 0.21 0.00 98.53 0.95 0.21 0.00 100.47 1.01 0.19 0.00 102.45 0.95 0.17 0.00 106.83 1.12 0.10 0.00 108.83 1.08 0.07 0.00 110.80 1.03 0.05 0.00 112.79 1.04 0.02 0.00 117.27 1.20 0.03 0.00 119.30 1.16 0.06 0.00 121.30 1.13 0.07 0.00 123.34 1.10 0.09 0.00 127.99 1.00 0.13 0.00 128.51 1.54 0.14 No 130.05 0.96 0.15 Contribu 130.51 1.46 0.15 132.10 0.93 0.16 132.57 1.38 0.17 134.16 0.93 0.18 134.50 1.35 0.18 138.64 1.05 0.21 139.12 0.95 0.22 140.74 1.03 0.22 141.20 0.94 0.23 142.79. 1.01 0.24 143.14 0.92 0.18 144.85 0.99 0.26 145.23 0.88 0.26 149.39 0.90 0.30 149.90 1.47 0.30 151.48 0.88 0.31 152.02 1.43 0.31 153.54 0.87 <> 0.33 154 FIGURE 5-13. Continued 319 MeV C.M. S t a t i s t i c a l Double Scattering D i f f r a c t i o n Angle Error and Attenuating Peg. % % % 153.90 1.39 0.33 No 155.62 0.84 0.40 Contribution 155.97 1.37 0.34 160.10 0.76 0.38 160.69 0.72 0.38 162.21 0.74 0.40 162.72 0.70 0.40 164.26 0.71 0.42 164.81 0.68 0.42 166.34 0.68 0.43 166.91 0.64 0.44 170.00 0.95 0.47 172.99 0.91 0.48 175.02 0.89 0.50 177.02 0.92 0.51 493 MeV 57.43 1.20 1.51 0.26 59.26 1.20 1.24 0.26 61.07 1.19 1.01 0.26 62.85 1.23 0.08 0.26 64.74 0.92 0.06 0.26 66.59 0.93 0.04 0.26 66.97 1.32 0.04 0.26 68.36 0.91 0.02 0.26 68.84 1.36 0.02 0.26 70.24 0.92 0.01 0.26 70.68 1.36 0.01 0.26 72.54 1.35 0.01 0.26 74.60 0.98 0.02 0.0 76.48 0.99 0.03 0.0 78.37 0.99 0.05 0.0 80.22 0.98 0.07 0.0 84.47 1.19 0.09 0.0 84.55 1.25 0.09 0.0 86.34 1.21 0.10 0.0 86.50 1.23 0.10 0.0 86.64 1.67 0.10 0.0 88.22 1.22 0.11 0.0 88.33 1.21 0.11 No 88.55 1.67 0.11 Contribution 90.14 1.22 0.11 90.29 1.26 0.11 90.48 •1.78 0.11 92.34 1.67 0.14 155 FIGURE 5-13. Continued CM. S t a t i s t i c a l Double Scat Angle Error and Attenu Deg. % % 94.50 1.19 0.19 96.48 1.19 0.29 96.82 1.39 0.31 98.43 1.19 0.37 98.77 1.37 0.37 100.44 1.20 0.38 100.64 1.42 0.39 102.66 1.38 0.39 104.96 1.25 0.38 106.89 1.30 0.35 108.87 1.23 0.32 110.91 1.23 0.28 115.66 1.39 0.17 117.56 1.33 0.13 117.81 1.43 0.12 119.61 1.30 0.09 119.79 1.40 0.08 121.68 1.26 0.04 121.86 1.36 0.03 123.83 1.30 0.01 128.46 1.30 0.12 130.57 1.29 0.15 132.64 1.24 0.19 134.76 1.16 0.23 137.47 1.24 0.27 139.42 1.37 0.30 139.55 1.21 0.31 141.54 1.31 0.33 141.65 1.14 0.33 143.65 1.26 0.36 143.80 1.11 0.36 145.75 1.23 0.38 153.71 1.26 0.48 155.89 1.23 0.50 158.00 1.18 0.52 160.15 1.17 0.54 165.12 1.34 0.57 167.29 1.32 0.59 169.39 1.20 0.62 171.55 1.13 0.64 493 MeV ing D i f f r a c t i o n ng % No Contribution 156 TABLE 5-14 Summary of Errors on To t a l Energy Data 319 MeV CM. S t a t i s t i c a l Double Scattering D i f f r a c t i o n Interaction Angle Error and Attenuation T a i l Degrees % _ % % % 66.74 0.86 0.36 0.18 0.21 68.65 0.82 0.38 0.14 0.20 70.50 0.85 0.40 0.11 0.19 72.32 0.85 0.41 0.08 0.17 493 MeV 57.49 1.40 0.15 0.08 0.18 59.32 1.30 0.12 0.06 0.18 61.12 1.53 0.10 0.05 0.19 62.96 1.59 0.08 0.04 0.19 157 Varying the normalization does not change the shape of the data, rather i t changes every point by the same fa c t o r . The uncertainty of the nor-malization depends on the cuts, s t a t i s t i c s and r e p r o d u c i b i l i t y of the -zero degree data as well as on the uncertainty i n the target length and density. The normalization error i s quoted separately from the error on the s i g n a l . The normalization error for the proton data depends both on the zero degree neutron runs and the absolute c a l i b r a t i o n of the e f f i c i e n c y . The expression f o r the normalization i s n t N(o-)u Thus, the normalization error on the proton data i s the normalization error on the neutron data plus the error on the absolute c a l i b r a t i o n of the e f f i c i e n c y . The discussion so f a r assumes the monitors have remained constant throughout the neutron and proton experiments; a study of possible monitor v a r i a t i o n was made. A l l of the factors e f f e c t i n g the normalization are summarized along with the estimated errors at 319 and 493 MeV i n table 5-15. The uncertainty i n the number of protons per unit area i n the target depends on the uncertainty i n the target length and density. As discussed i n V - l and V-2, the errors are 0.50% and 0.58% r e s p e c t i v e l y . The zero degree neutron data were analyzed with the same procedure as the scattered neutron data and so the error analysis of V-9 was followed c l o s e l y . The number of counts detected was corrected f o r attenuation by the l i q u i d hydrogen target Cfor target f u l l runs) and the number of moni-tor counts was corrected f o r the beam-off background. The r a t i o was computed f o r each run and the s t a t i s t i c a l errors were added i n quadrature with the uncertainties on the corrections. The weighted mean r a t i o and 158 TABLE 5-15 Summary of Normalization Errors Description 319 MeV 493 MeV 1. S t a t i s t i c a l Error on 0° Runs 0.86% 0.72% 2. Re p r o d u c i b i l i t y of 0° Runs 0.0% 0.65% 3. Pl-RF TOF Cut - 0° 0.38% 0.40% 4. Cut on Carbon Area - 0° 0.10% 0.22% 5. Cut on 6 - 0° 0.15% 0.13% c 6. Cut on P1-P2 TOF Cut - 0° 0.07% 0.17% 7. Target Length 0.50% 0.50% 8. Target Density 0.58% 0.58% Tot a l f o r Neutrons 1.3% 1.3% 9. Monitor S h i f t 2.24% 0.85% 10. E f f i c i e n c y V a r i a t i o n with Energy 0.46% 0.22% 11. E f f i c i e n c y S t a t i s t i c s 0.64% 0.69% 12. Choice of F i t 0.68% 0.83% Tot a l f o r Protons 2.8% 2.2% 159 2 2 was calculated f or both energies. The X was 1.54 on f i v e points at 319 MeV and 29.14 on sixteen points at 493 MeV. Consequently the error on the mean r a t i o at 493 MeV was increased by a factor of 1.35. The analysis of the uncertainty introduced by the cuts on the PI to P2 TOF, the f i d u c i a l area of the carbon, the sca t t e r i n g angle i n the car-bon and the PI to RF TOF was s i m i l a r to that of section V-9. The error estimated f o r the PI to P2 cut was 0.07% to 0.17% and 319 and 493 MeV res p e c t i v e l y . Figure 5-8 i l l u s t r a t e s the v a r i a t i o n i n N(0°)/M(0°) as a function of the cut p o s i t i o n and normalized to the r a t i o used i n the data analysis. The uncertainty due to the carbon cut was 0.10% at 319 MeV and 0.22% at 493 MeV respectively. Figure 5-9 shows the v a r i a t i o n i n M(0°)/N(0°) as a function of the accepted area of carbon normalized to the r a t i o at the +200 mm cut. The v a r i a t i o n of the zero degree data as a function of the 6C cut (the s c a t t e r i n g angle i n the carbon convertor) was determined by comparing the r a t i o , N(0°)/M(0°), with 17, 16 and 15 degree cuts. The er r o r , estimated as the change between the 17 and 16 degree cuts, was 0.15% at 319 MeV and 1.65% at 493 MeV. The PI to RF cut on the low energy side of the peak was varied by +.4 ns(+2 channels) and the average percent diff e r e n c e was 0.38% at 319 MeV and 0.40% at 493 MeV. The estimated t o t a l error on the normalization of the neutron data was a l l of the contributions discussed added i n quadrature, 1.3% and 2.2% at 319 and 493 MeV re s p e c t i v e l y . The normalization of the proton data also depends on the e f f i c i e n c y measurement and the r e l a t i v e s t a b i l i t y of the neutron beam monitors between the two data taking periods. The uncertainties introduced by these e f f e c t s VARIATION OF NORMALIZATION WITH PI TO P2 TOF CUT 1.0 m 0.9 UJ 0.8 h 319 MeV 160 170 CHANNEL 180 0.9 0.8 h 160 493 MeV x 170 CHANNEL FIGURE 5-8 Fractional change in the normalization as the cut on the PI to P2 TOF is var 161 10 UJO-9 < x o —J < 10 o 1 0 9 0-8 "» 1 1— 1 1 i 1 • — r 319 MeV 493 MeV 60 80 100 120 140 160 180 2 00 (mm) VARIATION OF N O R M A L I Z A T I O N WITH C A R B O N C U T F I G U R E 5-9 Fractional change in the normalization as the aotive area of the carbon convertor is varied . 162 are discussed below. The uncertainty on the e f f i c i e n c y was estimated from the s t a t i s t i c a l e r r o r, the v a r i a t i o n with energy and the v a r i a t i o n with the choice of function used to f i t the data. The s t a t i s t i c a l error on the e f f i c i e n c y at 319 and 493 MeV, calculated from the f u l l error matrix given i n table 4-2, was 0.64% and 0.69% r e s p e c t i v e l y . The change i n e f f i c i e n c y when the energy was v a r i e d by +2 MeV was 0.46% at 319 MeV and 0.22% at 493 MeV. The e f f i c i e n c y was calculated from each of the f i t s p l o t t e d i n f i g u r e 5-5, that were discussed i n section V-9. The standard deviation 2 and average were calculated with the worst f i t discarded. The X on the average was approximately one per point. The uncertainty due to the choice of the function was taken as the standard deviation divided by the average: 0.68% at 319 MeV and 0.83% at 493 MeV. The f i n a l source of error i n the proton data normalization was the r e p r o d u c i b i l i t y of the monitors between the neutron and proton sets of data. Figures 5-6 and 5-7 show the monitor r a t i o ("Wide Angle" Neutron Monitor to "In Beam" Neutron Monitor) at each energy for both the neutron and proton data. There was a s l i g h t s h i f t between the average neutron r a t i o and the average proton r a t i o that amounted to 2.24% at 319 MeV and 0.85% at 493 MeV. The sum of a l l of the normalization errors on the proton data added i n quadrature i s 2.8% at 319 MeV and 2.2% at 493 MeV. V-13. Results of the D i f f e r e n t i a l Cross Section Measurement The r e s u l t s of the d i f f e r e n t i a l cross section experiments and l i s t e d i n table 5-16 (table 5-17) and plotted i n f i g u r e 5-10 (figure 5-11) at 319 (493) MeV. The data presented i n these tables and figures are the corrected angles, the corrected cross sections and the t o t a l error. The normalization error has not been added to the error on the s i g n a l . 163 TABLE 5-16 D i f f e r e n t i a l Cross Section at 319 MeV CM. Angle D i f f e r e n t i a l Cross Section Degrees mb 11.13 5.126 + 0.364 16.42 4.853 + 0.160 32.43 3.964 + 0.104 48.33 3.101 + 0.079 62 .98 2.336 + 0.0 74 74.32 1.938 + 0.099 94.52 1.589 + 0.155 66.73 1.946 + 0.026 66.74 1.978 + 0.026 68.62 1.905 + 0.025 68.65 1.963 + 0.026 70.47 1.841 + 0.025 70.50 1.883 + 0.025 72.32 1.765 + 0.024 72.33 1.776 + 0.024 76.59 1.659 + 0.023 78.40 1.609 + 0.022 80.33 1.572 + 0.022 82.26 1.581 + 0.022 86.62 1.459 + 0.024 88.45 1.514 + 0.025 90.29 1.495 + 0.025 92.26 1.485 + 0.025 96.55 1.492 + 0.021 98.53 1.544 + 0.021 100.47 1.582 + 0.022 102.45 1.587 + 0.021 106.83 1.699 +- 0.025 108.83 1.757 + 0.025 110.80 1.850 + 0.026 112.79 1.922 + 0.027 117.27 2.092 + 0.032 119.30 2.235 + 0.033 121.30 2.299 + 0.034 123.34 2.451 + 0.035 127.99 2.799 + 0.038 128.51 2.795 + 0.050 130.05 2.902 + 0.039 130.51 3.014 + 0.052 132.10 3.105 + 0.041 132.57 3.188 + 0.053 134.16 3.240 + 0.043 134.50 3.415 + 0.056 138.64 3.729 + 0.053 139.12 3.808 + 0.051 140.74 3.865 + 0.054 164 TABLE 5-16. Continued CM. Angle D i f f e r e n t i a l Cross Section Degrees mb 141.20 4.030 + 0.054 142.79 4.040 + 0.056 143.14 4.148 + 0.055 144.85 4.249 + 0.059 145.23 4.408 + 0.057 149.39 4.664 + 0.062 149.90 4.626 + 0.081 151.48 4.861 + 0.064 152.02 4.899 + 0.085 153.54 5.047 + 0.066 153.90 5.176 + 0.088 155.62 5.331 + 0.070 155.97 5.331 + 0.090 160.10 5.906 + 0.074 160.69 6.092 + 0.075 162.21 6.205 + 0.078 162.72 6.441 + 0.079 164.26 6.753 + 0.084 164.81 6.944 + 0.085 166.34 7.396 + 0.091 166.91 7.627 + 0.092 170.00 8.854 + 0.124 172.99 9.802 + 0.136 175.02 10.519 + 0.145 177.02 10.879 + 0.152 165 10 8 d a mb/sr 6 \1 4 0 -1 1 1 1 r n p — * np i DIFFERENTIAL CROSS SECTION 319 MeV — NEUTRON NORMALIZATION ERROR 10.013 i • PROTON NORMALIZATION ERROR t 0.028 A > • • I f ; 4 t - / • - / -• -" — — i 1 • 0 60 120 DEGREES cm FIGURE 5-10 180 166 TABLE 5-17 D i f f e r e n t i a l Cross Section at 493 MeV CM. Angle D i f f e r e n t i a l Cross Section Degrees mb  17.06 5.674 ± 0.277 22.59 4.993 ± 0.220 28.12 4.517 ± 0.197 50.01 3.128 ± 0.134 66.03 2.080 ± 0.094 96.75 1.219 ± 0.075 57.43 2.373 ± 0.045 57.49 2.337 ± 0.047 59.26 2.266 ± 0.043 59.32 2.444 ± 0.048 61.07 2.212 ± 0.042 61.12 2.053 ± 0.043 62.85 2.043 ± 0.039 62.96 1.988 ± 0.043 64.74 2.003 ± 0.035 66.59 1.894 ± 0.033 66.97 1.884 ± 0.037 68.36 1.870 ± 0.032 68.84 1.772 ± 0.035 70.24 1.754 ± 0.030 70.68 1.707 ± 0.034 72.54 1.680 ± 0.033 74.60 1.627 ± 0.028 76.48 1.549 ± 0.027 78.37 1.481 ± 0.026 80.22 1.446 ± 0.025 84.47 1.262 ± 0.024 84.55 1.307 ± 0.025 86.34 1.242 ± 0.023 86.50 1.298 ± 0.025 86.64 1.275 ± 0.028 88.22 1.209 ± 0.023 88.33 1.208 ± 0.023 88.55 1.267 ± 0.028 90.14 1.217 ± 0.023 90.29 1.214 ± 0.023 90.48 1.143 ± 0.026 92.34 1.213 ± 0.027 94.50 1.105 ± 0.021 96.48 1.084 ± 0.021 96.82 1.100 ± 0.022 98.43 1.079 + 0.021 98.77 1.105 ± 0.022 100.44 1.054 ± 0.020 100.64 1.051 ± 0.022 167 TABLE 5-17. Continued CM. Angle D i f f e r e n t i a l Cross Section Degrees mb 102.66 1.063 + 0.022 104.96 1.089 + 0.021 106.89 1.056 + 0.021 108.87 1.110 + 0.021 110.91 1.119 + 0.022 115.66 1.220 + 0.025 117.56 1.274 + 0.025 •117.81 1.319 + 0.027 119.61 1.339 + 0.026 199.79 1.367 + 0.028 121.68 1.415 + 0.027 121.86 1.429 + 0.028 123.83 1.534 + 0.030 128.46 1.809 + 0.035 130.57 1.897 + 0.037 132.64 2.022 + 0.039 134.76 2.244 + 0.042 137.47 2.298 + 0.044 139.42 2.597 + 0.052 139.55 2.446 + 0.047 141.54 2.787 + 0.055 141.65 2.682 + 0.050 143.65 2.985 + 0.058 143.80 2.867 + 0.053 145.75 3.180 + 0.062 153.71 3.836 + 0.076 155.89 4.069 + 0.080 158.00 4.352 + 0.084 160.15 4.466 + 0.087 165.12 5.292 + 0.109 167.29 5.650 + 0.116 169.39 6.560 + 0.130 171.55 7.408 + 0.144 168 10 np • np d a 8 DIFFERENTIAL CROSS SECTION 493 MeV NEUTRON NORMALIZATION ERROR 10.013 PROTON NORMALIZATION ERROR 10.037 mb/sr V 0 0 60 120 DEGREES cm 180 FIGURE 5-11 169 These data w i l l be discussed i n chapter 7, where they w i l l be com-pared to previous experiments and the r e s u l t s of a phase s h i f t a n a l y sis. However, before the discussion of the error analysis i s concluded, the normalization i s checked by the two methods described i n 1-10, the overlap and the constraint that cr = aTv\ JLo- sm9 JLe 5 - 2 2 K W T I C Jo In. V-14. Overlap of Forward and Backward Data and the Total Cross Section Constraint The normalizations were studied by f i t t i n g the d i f f e r e n t i a l cross section by legendre polynomials of up to order 14, AS - S R.R [cos 9) 5 - 23 where the values of are given i n table 5-18 and figures 5-12 and 5-13 show the f i t s at 319 and 493 MeV res p e c t i v e l y p l o t t e d with the data. The overlap was evaluated by c a l c u l a t i n g the chi-square of the data points 2 i n the overlap range. At 319 MeV the % per data point was 1.5 with no normalization errors included. Adding the normalization errors i n qua-2 drature reduces the OC per data point to less than one, i n d i c a t i n g the normalization error i s consistent with the measured overlap. M7 W5 The e l a s t i c cross section was calculated by integr a t i n g the f i t (equation 5-23) ( T =a * T V ft 5 - 2 4 where A i s the c o e f f i c i e n t of P . The r e s u l t i s 35.67 + 1.01 mb for the o o — n-p e l a s t i c cross section at 319 MeV. The error was calculated as the 2 2 error on the c o e f f i c i e n t (+Q. 187) increased by the IC per point (% /n TABLE 5-18 Co e f f i c i e n t s of Legendre Polynomial F i t s to D i f f e r e n t i a l Cross Section at 319 and 493 MeV 170 Co e f f i c i e n t A, A. T.0 l l l l12 M.3 *14 Value at 319 MeV 2.45783 7.11052x10 2.02339 -8.09633x10 5.10558x10 -4.73299x10 2.17902x10 4.62635x10 3.05946x10 1.59414x10 2.86642x10 1.10831x10 1.55039x10 2.33594x10 5.05758x10 -1 -2 -1 -2 -1 -2 -1 -1 -1 -1 -1 -2 -2 Value at 493 MeV 2.39016 5.72969x10 1.90015 -1.56911x10 4.80779x10 -5.56631x10 1.96212x10 -1.30581x10 2.04288x10 3.23014x10 1.58674x10 7.75534x10 8.57518x10 -9.95165x10 3.76266x10 -1 -1 -1 -2 -1 -2 -1 -2 -1 -2 -2 -3 ^2 171 10 DIFFERENTIAL CROSS SECTION np—-np 319 MeV LEGENDRE POLYNOMIAL FIT 8 d a dXl mb/sr - H 60 120 DEGREES cm RGURE 5-12 180 172 10 e DIFFERENTIAL CROSS SECTION np-^np — LEGENDRE POLYNOMIAL FIT 493 MeV o1 l50~ 0 30 60 90 120 DEGREES cm FIGURE 5-13 180 173 = 1.085) i n quadrature with the normalization error (+.990). The i n e l a s -t i c cross section was calculated from the data i n the compilation -of Bystricky and Lehar Bt.o be 0.3 + 0.03 mb at 319 MeV. The t o t a l cross section, the sum of e l a s t i c and i n e l a s t i c cross sections i s 35.67 + 1.01 mb which i s i n excellent agreement with the measured t o t a l cross section (described i n chapter 6) of 36.40 + .27 mb. The normalization error at 319 MeV i s consistant with both the over-lap and the t o t a l cross section constraint at the one standard deviation l e v e l . At 493 MeV an extra point was included to constrain the f i t i n the forward region. The forward neutron data at 16.42, 32.43, 48.33, 62.98 and 74.32 degrees are f i t t e d by a s t r a i g h t l i n e with a l i n e a r c o r r e l a t i o n c o e f f i c i e n t of 0.998. The Legendre polynomial f i t based on only the r e a l data had a large o s c i l l a t i o n between 30 and 40 degrees. Therefore a l i n e a r extrapolation was made and an ad hoc point was added at 39.07 degrees. The f i t i s plotted with the data i n f i g u r e 5-13. 2 The K. per data point f o r the overlap region was 1.61. A s u f f i c i e n t normalization error, added i n quadrature with the error on the s i g n a l , 2 to reduce the X to one per point was 3.7%. This i s larger than the calculated 2.2% normalization error. The t o t a l cross section c a l c u l a t i o n confirmed the 3.7% normalization. The e l a s t i c cross section was calculated from A to be 30.04 + 1.18 mb o '.-.'hore the error was the normalization uncertainty (3.7%) added i n qua-2 drature with the error on the c o e f f i c i e n t (+.324) increased by the 7C (1.4 per p o i n t ) . The i n e l a s t i c cross section was calculated to be 4.15 B2 + 0.61 mb from compiled data . Thus, agreement at the one standard deviation l e v e l of the calculated t o t a l cross section with the measured • t o t a l cross section requires a normalization error of 3.7% since the 174 measured total cross section is 35.66+0.29 mb and the calculated is 34.19 + 1.31 mb. The overlap and total cross section constraint both indicate a normalization error of 3.7%. Thus the 2.2% error, calculated from the estimates of individual sources of error, i s too low. The most likely source of error to be underestimated was the efficiency measurement at 500 MeV. The normalization error on the proton data at 493 MeV is increased to 3.7%. The differential cross section data and the total cross section data w i l l be compared to previous world data and a phase shift analysis in chapter 7. 175 VI. Total Cross Section Experiment VI-1. Introduction to P r i n c i p l e s of Experimental Method The t o t a l cross section was measured at s i x energies by a trans-mission experiment. The TRIUMF neutron s c a t t e r i n g f a c i l i t y described i n chapter II was used. A schematic representation of the experiment i s shown i n f i g u r e 6-1. In a transmission experiment the r a t i o of beam f l u x f o r target f u l l and empty i s measured. The attenuation of a beam due to nuclear c o l l i s i o n s i s given by where N i s the number of p a r t i c l e s remaining a f t e r the beam has passed through the target, i s the number of incident p a r t i c l e s , n f c i s the number of p a r t i c l e s per unit area i n the target assuming that no target p a r t i c l e i s i n the shadow of any other, and <T i s the t o t a l nuclear cross section. The rate of incident p a r t i c l e s i s proportional to the count rate of the neutron beam monitor 6 - 2 where k Is a constant of p r o p o r t i o n a l i t y and M i s the count rate of the monitor. The number of p a r t i c l e s per unit area i s given by n t = NoZ> e - 3 ' fl where i s Avo.gadro's number, p i s the density of the target material, A i s the atomic mass In a.m.u., W i s the number of atoms per molecule and t i s the thickness of the material. Thus, f or an empty target f l a s k containing only hydrogen gas at a density p ^, the number of detected neutrons per unit time i s SCHEMATIC OF TOTAL CROSS SECTION EXPERIMENT FIGURE 6-1 177 N R = c 1 e e 4a — i l ^  v- w 6 "~ 4 where g 1 i s the t o t a l attenuation per incident p a r t i c l e f o r a l l of the material upstream of the target, ^"~'^'t^*«"f i s the attenuation due to the hydrogen gas (density Q G ) i n the l i q u i d l i q u i d hydrogen target and g_ * i s the t o t a l attenuation downstream of the target. When the l i q u i d hydrogen target i s f u l l (density j? j), the number of detected neutrons per unit time i s K I F -2<Mn -n to^. ? -£rbcr. i j ^ — - • * x v» v. 6 5 where 6 i s the attenuation due to the l i q u i d hydrogen. Dividing equation 6-5 by 6-4 y i e l d s 6 - 6 Substituting 6-2 and 6-3 into t h i s expression eliminates the unknown ^ and quantities  giving = ML tXKttfu"A>°^'  6"1 where i s the atomic mass of hydrogen. Equation 6-7 rel a t e s the t o t a l cross section to experimentally measured observables. Simply i n v e r t i n g equation 6-7 gives the neutron proton t o t a l cross section e x p l i c i t l y cr te - f U i t / Ni Mr ^  . R4 178 The s t a t i s t i c a l error derived from a Poisson d i s t r i b u t i o n i s given by t-cr =J3M£ / J L + - L + J _ + J _ N 6 _ 8 B VI-2. Apparatus and Re a l i z a t i o n The neutron detector, which i s i l l u s t r a t e d schematically i n f i g u r e 6-2, i s described i n an upstream to downstream order. The f i r s t s c i n t i l l a t o r , denoted DV, was a large veto (3.2 mm thick by 750 mm high by 360 mm wide) for incident charged p a r t i c l e s . The veto was b u i l t such that any l i n e through a l l of the rest of the detector must go through the veto. The neutrons were converted i n t o charged p a r t i c l e s i n a piece of CPL, 125 mm t h i c k by 250 mm square mounted immediately downstream of the veto. Following the convertor was a four counter telescope, each s c i n -t i l l a t o r 250 mm square by 3.2 mm thick. The f i r s t two counters were adjacent to the CIL, and were mounted h o r i z o n t a l l y with t h e i r l i g h t guides on opposite sides of the neutron beam. The signals from these two s c i n t i l l a t o r s , Dl and D2, were averaged to give a position-independent timing pulse; also, accidental coincidences from cerenkov l i g h t i n the tubes were avoided by t h i s arrangement. Adiabatic l i g h t guides were used to optimize the timing r e s o l u t i o n . The t h i r d and fourth detectors, D3 and D4, were mounted 0.61 m downstream of Dl and D2. The two counters were separated by 16 mm of aluminium to range out low energy background neutrons. Figure 6-3 i s a diagram of the e l e c t r o n i c l o g i c showing the d e f i n i t i o n of the t r i g g e r and the quantities scaled, The neutron monitor, constructed s i m i l a r l y to the detector, consisted 179 TOTAL CROSS SECTION NEUTRON DETECTOR DV CH, D2 Dl D3 D 4 3 ALUMINUM NEUTRON BEAM FIGURE 6-2 ELECTRONIC LOGIC FOR TOTAL CROSS SECTION DETECTOR FIGURE 6-3 181 of a veto 3.2 mm thick by 250 mm square, and a four s c i n t i l l a t o r t e l e -scope. The counters, known as MV, Ml, M2, M3 and M4 res p e c t i v e l y , were 250 mm square by 3.2 mm thick. The e l e c t r o n i c l o g i c for the monitor t r i g g e r d e f i n i t i o n and the scalers i s i l l u s t r a t e d i n f i g u r e 6-4. The incident proton beam monitor was the same as described i n chapter I I . A detected neutron had the signature DV-D1«D2-D3'D4 which was known as D (the e l e c t r o n i c l o g i c i s outlined i n f i g u r e 6-3). To increase the data c o l l e c t i o n rate, the D coincidence did not constitute an event that interrupted the computer. Instead, i t started a LRS QVT model 3001, which i s a N1M fast l o g i c time to d i g i t a l convertor and a multichannel analyzer. The time d i f f e r e n c e between D and the next RF cycle of the accelerator was histogrammed by the QVT(QVTl) f o r each t r i g g e r . The histogram was stored i n the i n t e r n a l memory of the device co n s i s t i n g of 1024 channels, each capable of storing a number up to 65,536 (64k). The histogram bins were 0.1 ns wide and a maximum of 50^xs was required to d i g i t i z e and store an event. The TOF started by the monitor s i g n a l M, defined as MV-M1-M2-M3>M4 and ended by the next RF cycle, was. stored in a histogram by a second QVT (QVT2). Both QVT's were co n t r o l l e d through a CAMAC int e r f a c e that enabled them to be started, stopped, read or cleared. The interf a c e s did not supply a "LAM" so i t had to be generated by an external source. The data a c q u i s i t i o n system performed the following functions. For each detected neutron, D, i t started QVT-1 which recorded the D to RF time of f l i g h t . A fixed 5Qjxs long busy s i g n a l was produced with, f a s t N1M l o g i c to gate o f f any futher neutron t r i g g e r s and to stop a l l the scalers marked i n figures 6-3 and 6-4 as i n h i b i t e d during the time the QVT was d i g i t i z i n g the time of f l i g h t . The e l e c t r o n i c l o g i c f o r t h i s i s shown i n f i g u r e 6-5. The. number of neutron triggers; was also scaled by 182 ELECTRONIC LOGIC FOR TOTAL CROSS SECTION MONITOR MV W M M2 M3 M 4 M \(234/ ME MV-MI234 43ns FIGURE 6-4 183 COMPUTER INHIBIT QVT INHIBIT 64 BIT SCALER START R F STOP LAM BUSY PDP 11/20 COMPUTER G A T E GENERATOR 50/AS NIM SIGNAL GENERATOR FAN OUT BUSY OUT INHIBIT ALL SCALERS INHIBITED SCALERS CRATE INHIBIT FIGURE 6-5 ELECTRONIC LOGIC FOR COMPUTER TRIGGER 184 a 15 b i t s c a l e r located i n a s p e c i a l " t r i g g e r s l o t " of the CAMAC crate. When t h i s s c a l e r overflowed, i n d i c a t i n g 64k neutrons having been counted, a "LAM" was generated that interrupted the computer. A computer interrupt i n i t i a t e d the following procedure. An i n h i b i t was fanned out to gate the D to RF TDC (QVT-1), the M to RF TDC (QVT-2) and a l l of the s c a l e r s . The on-line computer program stopped and read both QVT's and the sc a l e r s . A f t e r the data was transformed to a memory buffer the QVT's were cleared and restarted. A busy clear s i g n a l was then generated that removed a l l of the i n h i b i t s and allowed data taking to continue. A data c o l l e c t i o n rate of 5000 per second was possible with t h i s technique. The on-line computer code displayed the l a s t TOF spectrum read from QVT-1 and QVT-2. I t also formed an "on-line sum" histogram f o r both QVT's that contained a channel-by-channel sum of a l l the data taken up u n t i l then i n the run. Af t e r each event was read, i t was copied to magnetic tape. Therefore, a run was equivalent to a tape f i l e that consisted of a block for each event of 64k neutron t r i g g e r . Data was" c o l l e c t e d at the following s i x primary proton beam energies: 23Q, 280, 330, 379, 429, and 505 MeV. Data c o l l e c t i o n times ranged from 30 to 60 minutes and the runs were taken a l t e r n a t e l y with target f u l l and empty. The number of computer interrupts per run was between 100 and 200 corresponding to a rate of about 15 seconds per i n t e r r u p t . VI-3. O f f - l i n e Analysis The data was analyzed o f f - l i n e using the Amdahl 470 V/6 at UBC. A two pass system was developed. The f i r s t computer code read the data from the tape. For each block the D to RF TOF spectrum was read and the nearly monoenergetic neutron peak was found. The peak channel was calculated by searching f i r s t f o r the channel with the maximum number of 185 counts. The centroid or weighted mean channel was computed using the f u l l width at 10% of the maximum as the l i m i t s . The peak was integrated over +30 channels from the centroid. The value of the i n t e g r a t i o n f or target f u l l (empty) runs i s denoted N. (N? T) where i i s the block or event number. The number read from the scaler block for the monitor M i s c a l l e d M. 'off1 ) f o r target f u l l (empty) runs. The i n t e g r a t i o n of the peak and the value of the monitor for each block are written to a disk f i l e as an array for each run. The f i r s t - p a s s program also printed out four histograms which were inspected f o r each run. The centroid channel was histogrammed. Broad or double peaked centroid d i s t r i b u t i o n s indicated an RF s h i f t or a s h i f t i n phase of the beam with respect to the RF accelerating voltage. The second moment, calculated from the same channels as the centroid, was also histogrammed. RF s h i f t s that occurred during an event showed up as a second peak, whereas the f i r s t peak r e f l e c t e d the normal v a r i a t i o n of the width of the peak. These blocks are removed from the data l a t e r as anomalous values of N./M.. The channel-by-channel sum of a l l the blocks i n each run was histogrammed. In one of these, the raw D to RF TOF spectra were added together unchanged, while i n the other, a l l of the TOF peaks were s h i f t e d to a common channel. The second computer code read the disk output of the f i r s t program for a l l of the runs at a p a r t i c u l a r energy. The number of neutrons de-tected i n the peak (N^) per monitor (M^) was calculated f or each block In a run and i s given by for f u l l (empty) runs. The error was calculated using Poisson s t a t i s t i c s and i s given by MI 6 - 9 186 DMMT> / I I \ 6 - 1 0 for f u l l (empty) runs. The block number followed by N., M., R. and the respective errors 1 1 1 was pr i n t e d out. The weighted mean of N, M and R was calculated f o r each run as well as the error on the weighted mean, the standard deviation 2 and'the chi-square ( X ). The formulae used f o r the weighted mean and error are < X > =• £ X i 1 ti. e<x>= y^V 6 - 1 1 6 - 1 2 2 where x. represents N., M. or R.. The iL was calculated with the I. i i I following expression, \—e Runs with large values of the chi-square s t a t i s t i c were checked f o r RF s h i f t s . In a l l cases, the histograms from the f i r s t pass program indicated RF s h i f t s . The blocks that were affected were i d e n t i f i e d by high p a r t i a l chi-squares f o r p a r t i c u l a r values of R^ and were removed from the analysis. The t o t a l cross sections were calculated d i r e c t l y from R using equation 6-8 rewritten as c e - _ B - M <*"T)>\ 187 and ==__H«l / *•<»">; + 6 <R'>: 6 - 1 5 where the index j r e f e r s to a p a i r of adjacent runs with the target f u l l (empty) and then empty ( f u l l ) . Consecutive runs with the same target condition were combined by c a l c u l a t i n g the weighted mean. Table 6-1 gives the incident neutron beam energy, l i s t s the values of O"^  f o r that np energy, and includes the weighted mean value of the t o t a l cross section (.Cf =^^"np^' t * i e e r r o r o n t n e m e a n and the JC . The chi-square per data point i s larger than one, which indicates that the C 2 's are d i s t r i b u t e d about the mean with a larger deviation np 6 than i s estimated using Poisson s t a t i s t i c s . Because there i s a number of measurements of O" at each energy, an estimate of the error on the np a j ' mean of CF i s given by the width of the d i s t r i b u t i o n . The error c a l -np culated by t h i s method i s given by multiplying -^<OVp> by fl.' where n i s the number of data points. Table 6-2 summarizes the neutron beam energy, the t o t a l cross section and the chi-squared corrected error. The wider d i s t r i b u t i o n has been used as an i n d i c a t i o n of beam i n s t a b i l i t y . The data at 417 MeV was analyzed with one extra step. The values F MT of R_. and are plotted i n f i g u r e 6-6 against the time the runs were started at. The l i n e s are the r e s u l t s of l i n e a r least squares f i t s . They were parameterized by p . — V . T 0 5 y i o " H " t 6 - 17 6 - 1 6 TABLE 6-1 Table of Total Cross Sections Calculated from each Consecutive Pair of Full-Empty Runs Tot a l Cross Sections (mb) 493 MeV 417 MeV 369 MeV 38.62 ± 1.38 35.21 + 3.29 35.74 ± 0.71 35.23 ± 1.03 34. 91 + 2.31 35.18 ± 0.71 35.33 ± 0.84 34.86 + 2.31 33.12 ± 0.75 34.59 ± 0.76 34.75 + 3.27 36.16 ± 0.83 34.29 + 2.31 36.59 ± 0.87 34.16 + 2.32 34.21 ± 0.95 34.17 + 2.32 34.01 ± 0.84 34.02 + 2.21 35.45 ± 0.84 33.83 + 2.15 35.28 ± 0.84 33.66 + 2.32 35.17 ± 0.73 33.60 + 2.32 Average Average Average 35.33 ± 0.26 34.22 + 0.73 34.73 ± 0.42 = 1.247 X 2 / n = 1.0 = 2.364 319 MeV 267 MeV 212 MeV 35.88 ± 0.67 37.51 + 0.58 39.36 ± 0.59 34.82 ± 0.69 36.25 + 0.67 43.75 ± 0.65 36.40 ± 0.69 41.14 + 0.67 36.00 ± 0.65 35.16 ± 0.59 37.14 + 0.67 32.72 ± 1.14 36.91 ± 0.69 37.45 + 0.67 41.28 ± 0.59 35.17 ± 0.69 38.98 + 0.67 47.76 ± 0.65 36.35 ± 0.59 39.49 + 0.67 41.91 ± 0.65 37.94 + 0.67 46.66 ± 0.59 38.29 + 0.47 42.17 ± 0.65 36.40 + 0.67 43.16 ± 0.80 37.54 + 0.64 41.22 + 0.65 34.54 + 0.61 36.21 + 0.61 Average Average Average 35.81 ± 0.25 37.79 + 0.17 42.08 ± 0.21 X2/n = 1.189 * 2 / n = 7.88 * 2 / n = 32.39 189 TABLE 6-2 Summary of Tot a l Cross Sections and Neutron Beam Energies Neutron Beam Energy Total Cross Section MeV mb 212 42.08 ± 1.20 267 37.79 ± 0.48 319 35.81 ± 0.27 369 34.73 ± 0.65 417 34.22 ± 0.73 495 35.33 ± 0.29 190 FIGURE 6-6 FULL AND EMPTY RATES AS A FUNCTION OF TIME AT 417 MeV 191 The chi-square per data point on each f i t was 10.204 and 7.679 respect. t i v e l y . Table 6-3 summarizes both the value of the f i t f o r each run, and the error. The error was calculated using equation 6-10 and m u l t i p l i e d by the square root of the chi-square per data point on the f i t . The same procedure as before was used to complete the analysis. Consecutive runs with the same target condition were combined by taking the weighted mean and then CT^ was calculated f o r adjacent pairs of np target full-empty runs. The weighted mean and error were calculated and the r e s u l t s are l i s t e d i n table 6-2 along with the other energies. VT-4. Corrections and Systematic E f f e c t s There are three calculated corrections to the t o t a l cross sections. They are f o r : hydrogen gas i n the empty LIL, target f l a s k , f i n i t e s o l i d angle of the neutron detector f o r neutrons that e l a s t i c a l l y scattered through small angles and f o r i n e l a s t i c a l l y scattered neutrons. The c o r r e c t i o n f o r hydrogen gas i n the target has already been written e x p l i c i t l y i n t o the expressions used to c a l c u l a t e the t o t a l cross s e c t i o n , p ^ becoming j? ^ ~ P G' T n e v a-'- u e °^ P Q discussed i n chapter V. The correction i s 0.78%;~ - _ - " I n e l a s t i c neutrons that scattered into the s o l i d angle of the detector were a n e g l i g i b l e contribution ( <. .1%). This was calculated by 2 assuming a phase space d i s t r i b u t i o n modified by the terms (p^ cos©, ) 2 (p^cos 8* ) and a term i n momentum to approximate A production. The cosine terms give forward peaking while leaving the reaction symmetric with respect to the two f i n a l state nucleons. The symmetry i s required because the i n e l a s t i c f i n a l state i s known to be predominately i s o s p i n 1. The number of neutrons that scattered e l a s t i c a l l y but were s t i l l detected i s given by 192 TABLE 6-3 Table of Data and the Results of a Linear F i t at 417 MeV Target F u l l Time Data F i t ±Error (Hours) (N/M) (N/M) xl0~3 1.82 0.66258 0.66194 0.16774 2.73 0.66275 0.66182 0.16004 3.03 0.66118 0.66178 0.15753 4.83 0.66129 0.66154 0.14284 7.00 0.66206 0.66126 0.12618 15.31 0.65927 0.66016 0.08495 17.06 0.65997 0.65993 0.08423 18.45 0.66064 0.65975 0.08615 19.72 0.65763 0.65958 0.08972 21.48 0.66022 0.65935 0.09714 23.46 0.65683 0.65909 0.10825 24.50 0.65931 0.65895 0.11498 26.33 0.66003 0.65871 0.12797 28.00 0.65838 0.65849 0.14079 Target Empty 2.33 0.68284 0.68159 0.19391 3.73 0.67982 0.68135 0.17972 4.58 0.68153 0.68121 0.17130 5.90 0.68135 0.68098 0.15856 7.95 0.68155 0.68063 0.13985 16.10 0.67967 0.67924 0.09328 17.92 0.67944 0.67893 0.09354 18.97 0.67788 0.67875 0.09586 20.53 0.67725 0.67849 0.10197 22.20 0.67924 0.67820 0.11147 22.79 0.67766 0.67810 0.11543 25.47 0.67888 0.67764 0.13639 27.17 0.67679 0.67736 0.15154 19.3 _NjL = Ni e Y V t ^ a t \ d c r A ? cLXl . 6 - 1 8 where d-o^/oUl i s the e l a s t i c np d i f f e r e n t i a l cross section, Xi. i s the s o l i d angle of the neutron detector, n t i s the number of hydrogen gas atoms i n the empty LH^ target, n^ i s the number of hydrogen atoms i n the f u l l l i q u i d hydrogen target, and N^^* i - s t n e number of i n c i -dent neutrons approximated by the target empty rate. Therefore the expression f o r the t o t a l cross section given i n equation 6-8 i s modified to *N.V\.-/».H \ N; / K ~ MT/M*« ) 6 - 1 9 The neutron rate with the target f u l l i s within 3% of the target empty. Substituting t h i s into the co r r e c t i o n term y i e l d s the f i n a l expression. o-. T=-B»* UJNrMlUJLJ.-tfYl 6 . 2 0 The value of the d i f f e r e n t i a l cross section at zero degrees was predicted by a phase s h i f t a n a l y s i s at 215, 325, 425 and 515 MeV. These points are pl o t t e d i n fi g u r e 6-7. A f i t by eye was drawn through these points to in t e r p o l a t e to other energies. Table 6-4 l i s t s the cor r e c t i o n i n mb to the t o t a l cross section. A 20% error was assigned to the c a l c u l a t i o n . The f i n a l corrected values of the t o t a l cross sections are l i s t e d i n table 6-5 and pl o t t e d i n f i g u r e 6-8. 40 gV(0=O) d X 1 L A B mb/sr 200 500 MeV 300 400 FIGURE 6-7 DIFFERENTIAL CROSS SECTION AT ZERO DEGREES TABLE 6-4 Summary of Correction to To t a l Cross Section Gas i n Empty Target 0.77% I n e l a s t i c Contamination <0.01% F i n i t e S o l i d Angle of Detector Energy Correction MeV mb 212 .051 268 .048 319 .047 369 .048 417 .049 495 .058 TABLE 6-5 Corrected Values of To t a l Cross Section Neutron Beam Energy Total Cross Section MeV mb 212 42.46 + 1.20 268 38.18 ± 0.48 319 36.14 ± 0.27 369 35.05 ± 0.65 417 34.53 ± 0.73 495 35.66 ± 0.29 197 FIGURE 6-8 45 Total Cross Section cr , np TOT R 44 43 42 41 E 40 39 38 } 37 36 35 34 1 i I 33 l 200 300 400 500 NEUTRON KINETIC ENERGY (MeV) 198 VII. Discussion of Data and Conclusions In t h i s chapter the new.neutron-proton sc a t t e r i n g data at 319 MeV and 493 MeV described i n the foregoing chapters are compared with data, s i m i l a r i n energy, obtained at other l a b o r a t o r i e s . The e s s e n t i a l changes i n the phase s h i f t s extracted from the combined world data due to the i n c l u s i o n of the new data i s then described along with a com-parison of these new phase s h i f t s and the phase s h i f t s predicted from c a l c u l a t i o n s using the Paris p o t e n t i a l . S i m i l a r l y the t o t a l cross section measurements are compared to data obtained at other laboratories and the e f f e c t of the new data on the dispersion r e l a t i o n c a l c u l a t i o n s of G r e i n ^ i s discussed. VII-1. D i f f e r e n t i a l Cross Section at Energies Near 319 MeV The d i f f e r e n t i a l cross section at 319 MeV has an average error of 5% on the neutron data i n the forward region of the angular d i s t r i b u t i o n and 1.5% on the proton measurements i n the backward part of the angular d i s t r i b u t i o n . Normalization errors are 1.3% and 2.8% i n the respective regions. „ . _ A7,D1,B10,S8 c _ . Four previous measurements of the d i f f e r e n t i a l cross section made before the advent of the new generation of accelerators i n - t h i s energy region e x i s t . These previous r e s u l t s are plo t t e d i n fi g u r e 7-1 along with a smooth f i t to the new data. To f a c i l i t a t e the comparison of errors the new neutron points are plo t t e d but to improve the c l a r i t y of f i g u r e 7-1 only a sample of the proton data i s included. P r i o r to the experiments described here only the data of De Pangher^ covered the f u l l angular range. The data were measured by scat t e r i n g incident neutrons from hydrogen In a Wilson cloud chamber and the d i s t r i b u t i o n was; normalized to a t o t a l cross section of 35 mb. 199 10 9 8 v- 5 E 3 " D b T3 DE PANG HER 300 MeV I ASHMORE 350 MeV <j> PP.A. 309-6 MeV 4 P.P.A. 313 MeV \ NEW DATA SMOOTH CURVE THROUGH NEW DATA np np 20 40 60 80 100 120 140 160 180 DEGREES cm FIGURE 7-1 DIFFERENTIAL CROSS SECTION AT ENERGIES NEAR 319 MeV • 20Q The quoted e r r o r s , t y p i c a l l y 10%, do not include the uncertainty on the normalization rather, they are purely s t a t i s t i c a l . These data are i n remarkable agreement with the new data presented here between 35 and 145 degrees; outside of t h i s range the De Pangher data i s r e l a t i v e l y low. A l The Ashmore data from Liverpool are i n excellent agreement with the new data i n both shape and normalization. These data were normalized by f i t t i n g a quadratic polynomial to the energy dependence of the d i f -f e r e n t i a l cross section at 160.67°. The data f i t t e d , measured at 300°"*", H4 H5 D3 380 ' and 400 MeV, were absolutely normalized to the t o t a l cross section at each energy. The most precise measurement of the t o t a l cross A8 section i n the energy range of the f i t was made by Ashmore et a l and i s i n excellent agreement with the new t o t a l cross section measurements. The remaining two experiments are from the Princeton-Pennsylvania B10 Accelerator (PPA). The forward neutron measurements disagree with the new data i n shape. The quoted uncertainties are large, varying from 5% S8 to greater than 10%. The r e c o i l proton measurement was normalized absolutely with a c a l i b r a t e d neutron beam monitor. These data disagree both i n shape and normalization with the new data and Ashmore data. E l A measurement was also made at LAMPF of the r e c o i l proton d i s t r i -bution at 324.1 MeV. The d i s t r i b u t i o n plotted i n figu r e 7-2, agrees with the shape of the new data very w e l l , however the r e l a t i v e normalization of the LAMPF data i s low by 6%. Cl e a r l y the new data at 319 MeV has made a su b s t a n t i a l improvement to the world data. The p r e c i s i o n has been improved i n the range from 10 to 120 degrees and the absolute normalization has been determined to 1.3% for the neutron data and 2.8% for the proton data. 201 1 1 1 I 1 1 1 1 Differential Cross Sections at Energies Near 319 MeV | Lampf 324-1 MeV + New Data 315 MeV — Smooth Curve Through New Data ! 5 1 np np 20 60 100 Degrees cm Figure 7-2 140 180 •202 VII-2. D i f f e r e n t i a l Cross Section at Energies near 493 MeV At 493 MeV the new d i f f e r e n t i a l cross section data were-measured with an average p r e c i s i o n of 2.0% for the r e c o i l proton data and 5% f o r the neutron data. The normalization uncertainty was 3.7% and 1.3% res p e c t i v e l y . There are fewer previous measurements at 493 MeV and a l l are r e c o i l S8 E l proton experiments. The P.P.A. and LAMPF .. data are plo t t e d i n f i g u r e 7-3 along with a f i t to the new data. Some of the new points are included B i l f o r comparison of errors. The Bizard data from Saclay are-plotted i n figur e 7-4 along with a f i t to the new data. P.P.A. data at 466 MeV were absolutely normalized by a ca l i b r a t e d neutron monitor. The data do not agree i n shape with any of the other e x i s t i n g measurements nor with the data presented i n t h i s t h e s i s . No agreement i n shape e x i s t s even i n a r e s t r i c t e d range between 60 and 120 degrees where there are only the new and P.P.A. r e s u l t s . The LAMPF data was normalized by simultaneously measuring the e l a s t i c n p—»np rate and the i n e l a s t i c np—» Tt°d reaction rate. Isospin conser-v a t i o n i n the N-N i n t e r a c t i o n implies that the i n e l a s t i c production of deuterons from an n-p i n i t i a l state i s one h a l f the rate from pp—•Tf +d, a reaction involving only charged p a r t i c l e s and hence should be e a s i l y normalized absolutely. The new data agrees e x c e l l e n t l y with the shape of the LAMPF data but i s normalized 1.5% higher well within the quoted 7% uncertainty. The Saclay experiment was also normalized by comparison with the pp >. T T f d cross section and i s reported to have a 5% normalization. The new data agrees with the shape of the Saclay data but i s normalized 4% lower. There are two groups of points i n the Saclay data that show a large v a r i a t i o n i n the data, one near 160 degrees and the other near 203 10 DIFFERENTIAL CROSS SECTION AT ENERGIES NEAR 493 MeV 8 7 6 E C5 b 4 | j LAMPF 495-7 MeV 4 P.P.A. 466 MeV ! NEW DATA 493 MeV -SMOOTH CURVE THROUGH NEW DATA np np ^ * 0' 30 60 9 0 120 DEGREES cm 150 180 FIGURE 7-3 204 •o 0 9 DIFFERENTIAL CROSS SECTION AT ENERGIES NEAR 493 MeV • SACLAY 494-2 MeV 8H ! NEW DATA 493 MeV SMOOTH CURVE THROUGH NEW DATA i ,1 » 6r \ j E 51 l\ np *np j/ft 1 4r \ i 2h \* .1 f /T Ql 1 1 L 0 30 60 90 120 150 180 DEGREES cm FIGURE 7-4 205 175 degrees. To summarize, the d i f f e r e n t i a l cross section data at 493 MeV described i n t h i s thesis i s the f i r s t measurement i n the 15 to 55 degree range. The new data agrees very w e l l i n shape with LAMPF and Saclay between 120 and 175 degrees whereas the normalization agrees with LAMPF but i s lower than Saclay by one standard deviation. The P.P.A. cross sections do not agree i n shape with the data of t h i s thesis nor any other previous measurement. As the 55 to 120 degree range has been measured only at P.P.A. and TRIUMF, the disagreement of the PPA data at large angles renders i t suspect i n the ce n t r a l angular range as w e l l . VII-3. T o t a l Cross Section Data between 200 and 530 MeV B2 The previously measured neutron-proton t o t a l cross sections between 200 and 530 MeV are plotted i n f i g u r e 7-5 and l i s t e d i n table 7-1. The new data, also plotted i n figu r e 7-5, exhibits .a smooth energy v a r i a t i o n and i s i n agreement with.three previous precise measurements by K3 Aft R19 Kazarinov at 200 MeV, Ashmore at 351.5 MeV and Bugg at 516 MeV. The n-p t o t a l cross section was previously measured very p r e c i s e l y M8 at 9 energies by the P.P.A. group. The energy v a r i a t i o n of the P.P.A. data does not agree with the trend of the new data. The measurements of P.P.A., Kazarinov, Ashmore and Bugg are plotted i n figu r e 7-6 along with the new data. A cubic polynomial l e a s t squares f i t i n k i n e t i c energy to the P.P.A. data and a quadratic l e a s t squares f i t to the remaining points 2 i s shown as w e l l . The f i t to the P.P.A. data had a of 7.18 for 9. 2 points, a quadratic f i t to the same data had a TC of 11.67, whereas the quadratic f i t to the new data plus the other previously measured 2 precise data had a 7C of 2.58 for 9 data points. The c o e f f i c i e n t s of the f i t to the new data are l i s t e d i n table 7-2, to the P.P.A. data i n table 7-3. The energy dependence of the two curves- i s c l e a r l y not Total Cross Section cr np TOT K 45 • I 7 PREVIOUS WORLD DATA 40 1/ • • i • 35 [ I i , ' . 1 > / I' !• • • • f 30 / I . . 1 1 i 1 1 — 200 300 400 500 MeV Figure 7 - 5 PREVIOUSLY EXISTING WORLD DATA TABLE 7-1 Ex i s t i n g n-p To t a l Cross Section Measurements between 200 and 530 MeV Energy Total Cross Section Reference MeV mb 200 42.7 ±0.9 K3 208 37.0 ±2.0 D6 220 41.0 ±2.4 D4 220 41.3 ±3.5 M9 270 38.0 ±1.5 D5 270 33. ±3.0 F l 315 32.5 ±4.0 D6 351.5 35.6 ±0.7 A8 380 34. ±2.0 D7 380 31.0 ±1.5 -:_1.3 C4 408 31.6 ±2.0 M10 410 33.7 ±1.3 Nl 500 34. ±2.0 D7 516 35.72 ±0.26 B12 234.9 40.87 ± 1.26 S.I..N. 275.1 37.39 ± 1.06 i b i d 321.1 35.17 ±1.45 i b i d 366.7 33.43 ±2.03 i b i d 405.3 34.40 ±2.13 i b i d 445.0 32.27 ±2.03 i b i d 473.7 30.72 ±2.42 i b i d 247 42.80 ±1.02 P.P.A. 278 38.63 ±0.72 i b i d 311 37.32 ±0.60 i b i d 344 33.97 ±0.57 i b i d 379 34.09 ±0.26 i b i d 414 33.90 ±0.24 i b i d 450 33.57 ± 0.24 i b i d 488 34.16 ±0.24 i b i d 526 34.94 ± 0.24 i b i d TABLE 7-2 Co e f f i c i e n t s of F i t to New Total Cross Section :ino\ B12 K3 A8 Data plus Data of Kazari v , Ashmore and Bugg C o e f f i c i e n t s of Polynomial F i t i n K i n e t i c Energy A 63.3039 o A± -0.136337 A 2 1.61387xl0~ 4 TABLE 7-3 M8 Co e f f i c i e n t s of F i t to P.P.A. Total Cross Sections C o e f f i c i e n t s of Polynomial F i t i n K i n e t i c Energy A 1.07677 o A -0.448344 A 2 8.79226xl0~ 4 A 3 -5.51187x10"7 209 FIGURE 7-6 Cross Section o"T0T np ^ KAZARINOV ^ ASHMORE } BUGG { P. P. A. tji NEW DATA U B I C FIT TO RP.A. DATA 210 2 consistent; the X s t a t i s t i c f o r P.P.A. data compared to the new data plus world data i s 141 for the nine points. The t o t a l cross section i s rela t e d to the imaginary part of the scattering amplitude at zero degrees by the Opt i c a l theorem °--TOT = ^ fle - 'Oj OH 7 - 1 k where k and E are the momentum and energy of the incident neutron. The r e a l part of the forward s c a t t e r i n g amplitude i s rela t e d to the imaginary G 6 part by a dispersion r e l a t i o n that has been calculated by W. Grein Table 7-4 l i s t s the r e s u l t s of the dispersion r e l a t i o n analysis by Grein with and without the new data. The r e a l part of the forward scattering B13 amplitude calculated by the phase s h i f t analysis of Bugg i s now i n better agreement with the r e s u l t s of the dispersion r e l a t i o n , both l i s t e d 2 i n table 7-5. The X s t a t i s t i c has been reduced from 130 to 101, a change of 22%. VII-4. Phase S h i f t Analysis A phase s h i f t analysis of the "world data" without the new cross B 3 sections ("old PSA") i s given by Bugg at 210, 325, 425 and 515 MeV. A s i m i l a r a nalysis has been made at 142, 210, 325, 425 and 515 MeV with D2 D2 the new cross section data included at 210 , 325, 425 and 515 Mev. The set of world data used i n the analyses i s very s i m i l a r to that of A l A2 B3 Arndt's ' with a few exceptions . A l i s t comparing the new phase s h i f t s at 325 and 515 MeV with the old phase s h i f t s i s given i n table 7-6. The phase s h i f t analysis at 325 MeV had 455 data points, 433 degrees 2 of freedom and the X was 488.3. The r e a l part of the forward s c a t t e r i n g C3 amplitude calculated by Carter and Bugg was included as a constraint. The i n e l a s i t i c i t y was r e s t r i c t e d to the ^ T) p a r t i a l wave as suggested by 2 the isobar model. The % on the new d i f f e r e n t i a l cross section data TABLE 7-4 Results of Dispersion Relation Analysis i n the Intermediate Energy Range Lab. Old Analysis New Analysis Momentum Re F(o) Im F(o) Re F(o) Im F(p) GeV/c Gey" 1 GeV"1 GeV"1 Gev" 1 0.30 6.88 11.28 6.92 11.28 0.40 7.04 7.57 7.15 7.57 0.44 6.77 6.72 6.98 6.72 0.46 6.59 6.39 6.84 6.60 0.50 6.18 5.90 6.34 6.18 0.55 5.63 5.54 5.68 5.90 0.60 4.98 5.42 4.91 5.80 0.65 4.30 5.45 4.12 5.76 0.70 3.58 5.58 3.35 5.80 0.75 2.85 5.78 2.62 5.90 0.80 2.14 6.00 1.94 6.08 0.85 1.42 6.23 1.28 6.25 0.9.0 0.79 6.41 0.71 6.50 0.95 0.29 6.62 0.19 6.79 1.00 -0.13 6.89 -0.28 7.10 1.10 -0.84 7.73 -1.10 7.89 1.20 -1.63 8.75 -1.90 8.77 2.00 -6.86 16.27 -7.00 16.27 4.00 -14.85 32.94 -14.97 32.94 8.00 -22.75 64.68 -22.87 64.68 212 TABLE 7-5 Real Part of Forward Scattering Amplitude from P.S.A. and Dispersion Relation Energy Dispersion Relation P.S.A. MeV Old ReF(o) GeV" 1 New ReF(o) GeV - 1 . ReF(o) GeV" 1 142 5.79 5.87 5.52 ± . 1 2 210 4 .13 3.93 3.32 ± . 1 4 325 1.48 1.33 0 .15 ± . 1 4 425 - 0 . 4 -0 .18 -0 .15 ± . 1 3 515 -0 .91 -1 .18 -r l .00 ± .11 FIGURE 7-6 Phase S h i f t Analysis of World Data with and without New Cross Sections Phase S h i f t \ \ 3 3 V 4 V H, 325 MeV 515 MeV Old New Old New Degrees Degrees Degrees Degrees 0.95±0.78 0.95+0.62 -14.07+1.33 -13.5510.88 7.13±0.55 6.65±0.42 8.80+1.01 8.7710.61 -26.81±0.53 -25.33±0.36 -27.86±0.84 -26.02+0.53 -34.69±0.98 -34.07±0.21 -35.9011.41 -41.36+0.99 25.93±0.69 23.76+0.36 19.00+0.98 19.29+0.52 3.61±0.32 2.4110.26 2.56+0.40 3.05+0.31 6.98±0.26 7.57±0.17 8.1U0.41 7.96+0.26 -1.77±0.46 -4.3H0.21 -6.02+0.58 -6.22+0.27 -4.46±0.31 -5.83±0.18 -6.61+0.32 -6.37±0.18 7.22±0.42 7.48±0.23 7.8U0.56 8.2410.27 0.03±0.20 -0.33+0.14 -1.44+0.32 -1.43+0.18 -13.2210.65 -13.06±0.56 -28.67+0.93 -25.71+0.52 -9.83±0.50 -9.61±0.46 -22.33+0.83 -22.68±0.43 -30.45±0.37 -30.4810.29 -43.13+0.70 -40.7910.29 17.15±0.20 17.14+0.17 18.44+0.41 19.0410.23 -2.48±0.16 -2.34±0.15 -0.85+0.32 -0.72+0.20 0.87±0.24 0.67+0.18 -0.20+0.32 -0.68+0.19 9.94±0.16 9.92±0.15 12.76+0.20 13.19+0.14 -2.84±0.35 -2.47+0.25 -1.76+0.52 -1.6710.25 3.03±0.10 3.02±0.09 4.1210.10 4.28±0.07 -1.54±0.08 -1.54±0.072 -1.8H0.13 -1.97+0.072 0.7010.07 0.61+0.065 0.6910.10 0.4610.065 1.3210.10 1.46±0.083 2.64±0.14 2.93+0.068 -1.10±0.09 -1.17+0.079 -1.25+0.10 -1.47+0.079 0.54+0.07 0.47±0.061 0.73±0.07 0.72+0.061 0.999410.0013 0.9975+0.0013 0.889710.0102 0.8302+0.0063 FIGURE 7-7 PHASE SHIFTS 217 DEGREES 8 4 0 -4 1 T "T — i T 1 • / • 0 / O 6 3 ^ G / ° 4 / o i NEW o OLD — PARIS POTENTIAL o 3G 5 A • o 9 V • • e • o 3„ G 3 • » • • • • • 100 300 500 MeV FIGURE 7-10 PHASE SHIFTS 218 was 74.2 f o r 71 points. The PSA at 515 MeV had 561 data points, 538 degrees of freedom and 2 a % of 826.2. The new d i f f e r e n t i a l cross section proton data were renormalized i n t h i s analysis by a factor of 1.038, approximately one standard deviation of the uncertainty on the normalization, and a syste-matic error of 1% was added i n quadrature to a l l points. There was no constraint on the r e a l part of the forward scattering amplitude and the 1 2 i n e l a s t i c i t y was r e s t r i c t e d to the p a r t i a l wave. The *)£ for the cross section data at 493 MeV described i n t h i s t h e s i s was 91.0 for 75 points. Including the new cross section data i n the phase s h i f t analysis reduced the errors on a l l of the phase s h i f t s , with the 1=0 phase s h i f t s improved the most. The errors were calculated from the diagonal elements 2 of the error matrix and scaled up by the square root of the H per degree of freedom. Changes of more than one standard deviation occurred 1 "™" ™* 1 3 3 3 3 3 i n the P.. , 6 , E , F„, D. , D„, G„ and Gn isovector and P i s o s c a l a r 1 1 3 3 1 2 3 5 o phase s h i f t s at e i t h e r 325 or 515 MeV. Figures 7-7 to 7-10 show a l l of 3 the 1=0 phase s h i f t s up to G waves and the P q 1=1 phase s h i f t p l o t t e d as a function of energy f o r both the old and new PSA. The predictions of the Paris p o t e n t i a l are p l o t t e d with the experimental points. As the old BASQUE PSA was incorporated i n the P a r i s p o t e n t i a l as phenomenolo-g i c a l input, the S, P and D waves of the old analysis should be w e l l f i t by the p o t e n t i a l . However, the higher p a r t i a l waves, calculated theo-r e t i c a l l y , are less dependent on the old phase s h i f t s . 3 3 3 3 At 325 MeV the D^, G^ and G,. phase s h i f t s have a much smoother energy dependence than was indicated by the previous analysis. The a 1 1 °^ t ^ e ^ waves and the £ ^ mixing parameter have a l l moved s i g n i f i c a n t l y c l o s e r to the Paris: p o t e n t i a l c a l c u l a t i o n s . In p a r t i c u l a r , DEGREES 8 4 0 2 8 0 1 -T""- 1" 1 A / A —« 1 » • A A A A • • / A DL-S • ° T / * * / • * A • / i NEW ' / * OLD / — PARIS 1 i < i POTENTIAL 100 300 FIGURE 500 MeV 7-11 PHASE SHIFTS DEGREES 2.0 I • « — — H I — i r I NEW i OLD — PARIS POTENTIAL FIGURE 7-12 PHASE SHIFTS , 221 3 3 the and G,. phase s h i f t s have changed by more than 100% and now are s u b s t a n t i a l l y i n agreement with the predictions of the p o t e n t i a l . The analysis at 515 MeV produced s i m i l a r r e s u l t s , the ^ 1 ' ^ 1 ' 3 3 — G^. G,. and £ ^ a l l show a smoother energy dependence, e s p e c i a l l y i n the D and G waves. The d i f f e r e n t i a l cross section predominately a f f e c t s the c e n t r a l component of the N-N i n t e r a c t i o n . Figures 7-11 and 7-12 re s p e c t i v e l y show the D and G waves factored into the c e n t r a l , s p i n - o r b i t (L-S) and tensor combinations. Both the new and the old phase s h i f t analyses are plotted along with the predictions of the Paris p o t e n t i a l . The D^ (central) phase s h i f t s show a smoother dependence on energy which i s also seen i n the G waves, but not as c l e a r l y . A further study of the theo-r e t i c a l constraints on the G waves, such as one pion exchange, one boson exchange and coulomb b a r r i e r c a l c u l a t i o n s , may improve the G^ phase s h i f t s . The spin-o r b i t and tensor combinations show some improvement but are not as,strongly affected as the c e n t r a l part. VII-5. Conclusions The d i f f e r e n t i a l cross section data at 319 and 493 MeV are i n good agreement with most previous measurements but d i f f e r from the P.P.A. experiments. At 319 MeV the absolute normalization of the r e c o i l proton data i s +2.8% and +1.3% for the neutron data. Precise data has been presented i n the angular range between 10 and 120 degrees, reducing errors from 10% to 5% i n t h i s angular domain. Data at 493 MeV i s presented f o r the f i r s t time i n the angular range from 15 to 60 degrees. The data between 60 and 120 degrees con-f l i c t s with the only other measurement, P.P.A.. The absolute normali-zation of the r e c o i l proton data was established to +3.8% and 1.3% for the neutron data. 222 The t o t a l cross section data are i n good agreement with three previously measured precise data points and have a quadratic smooth energy dependence. The new t o t a l cross sections do not agree with the P.P.A. measurements. 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